解析函数的新积分算子
IF 1.9
3区 数学
Q1 MATHEMATICS
H. Özlem Güney, Shigeyoshi Owa, Adel A. Attiya
{"title":"解析函数的新积分算子","authors":"H. Özlem Güney, Shigeyoshi Owa, Adel A. Attiya","doi":"10.1155/2024/5295531","DOIUrl":null,"url":null,"abstract":"Let <svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 31.9134 14.7625\" width=\"31.9134pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,10.244,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,16.195,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,20.693,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,27.219,0)\"></path></g></svg> be the class of functions <svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 24.0049 12.7178\" width=\"24.0049pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,8.352,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.85,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,19.325,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> given by <span><svg height=\"17.0656pt\" style=\"vertical-align:-5.474199pt\" version=\"1.1\" viewbox=\"-0.0498162 -11.5914 35.086 17.0656\" width=\"35.086pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,8.352,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.85,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.325,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,27.455,0)\"></path></g></svg><span></span><svg height=\"17.0656pt\" style=\"vertical-align:-5.474199pt\" version=\"1.1\" viewbox=\"38.6681838 -11.5914 22.963 17.0656\" width=\"22.963pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,38.718,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,45.193,-5.741)\"><use xlink:href=\"#g50-113\"></use></g><g transform=\"matrix(.013,0,0,-0.013,54.05,0)\"></path></g></svg><span></span><svg height=\"17.0656pt\" style=\"vertical-align:-5.474199pt\" version=\"1.1\" viewbox=\"64.5361838 -11.5914 55.423 17.0656\" width=\"55.423pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,64.586,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,70.579,3.132)\"><use xlink:href=\"#g50-113\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,76.013,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,81.573,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,86.788,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,93.263,-5.741)\"><use xlink:href=\"#g50-113\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,98.697,-5.741)\"><use xlink:href=\"#g54-36\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,104.257,-5.741)\"><use xlink:href=\"#g50-111\"></use></g><g transform=\"matrix(.013,0,0,-0.013,112.378,0)\"><use xlink:href=\"#g117-36\"></use></g></svg><span></span><svg height=\"17.0656pt\" style=\"vertical-align:-5.474199pt\" version=\"1.1\" viewbox=\"122.8641838 -11.5914 75.481 17.0656\" width=\"75.481pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,122.914,0)\"><use xlink:href=\"#g113-98\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,128.907,3.132)\"><use xlink:href=\"#g50-113\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,134.341,3.132)\"><use xlink:href=\"#g54-36\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,139.901,3.132)\"><use xlink:href=\"#g50-111\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,144.56,3.132)\"><use xlink:href=\"#g54-36\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,150.12,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,155.145,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,161.62,-5.741)\"><use xlink:href=\"#g50-113\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,167.054,-5.741)\"><use xlink:href=\"#g54-36\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,172.614,-5.741)\"><use xlink:href=\"#g50-111\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,177.273,-5.741)\"><use xlink:href=\"#g54-36\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,182.833,-5.741)\"><use xlink:href=\"#g50-50\"></use></g><g transform=\"matrix(.013,0,0,-0.013,190.764,0)\"><use xlink:href=\"#g117-36\"></use></g></svg><span></span><svg height=\"17.0656pt\" style=\"vertical-align:-5.474199pt\" version=\"1.1\" viewbox=\"201.2501838 -11.5914 15.873 17.0656\" width=\"15.873pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,201.3,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,206.443,0)\"><use xlink:href=\"#g113-46\"></use></g><g transform=\"matrix(.013,0,0,-0.013,211.586,0)\"><use xlink:href=\"#g113-46\"></use></g></svg></span> which are analytic in the open unit disk <span><svg height=\"8.92059pt\" style=\"vertical-align:-0.2325001pt\" version=\"1.1\" viewbox=\"-0.0498162 -8.68809 12.183 8.92059\" width=\"12.183pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,9.074,0)\"></path></g></svg><span></span></span> For <span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 34.319 14.7625\" width=\"34.319pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,8.352,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,12.85,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.325,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,27.455,0)\"></path></g></svg><span></span><span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"37.9011838 -9.28833 32.021 14.7625\" width=\"32.021pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,37.951,0)\"><use xlink:href=\"#g113-66\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,48.195,3.132)\"><use xlink:href=\"#g50-113\"></use></g><g transform=\"matrix(.013,0,0,-0.013,54.146,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,58.644,0)\"><use xlink:href=\"#g113-111\"></use></g><g transform=\"matrix(.013,0,0,-0.013,65.17,0)\"><use xlink:href=\"#g113-42\"></use></g></svg>,</span></span> new integral operators <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 43.0414 14.8173\" width=\"43.0414pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,14.556,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,19.003,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,27.355,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,31.853,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,38.328,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 37.4604 14.8173\" width=\"37.4604pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.422,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.774,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,26.272,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.747,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> <span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 21.261 12.7178\" width=\"21.261pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,13.63,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"24.843183800000002 -9.28833 9.204 12.7178\" width=\"9.204pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,24.893,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,31.133,0)\"></path></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"36.2261838 -9.28833 9.204 12.7178\" width=\"9.204pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,36.276,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,42.516,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"47.6091838 -9.28833 9.204 12.7178\" width=\"9.204pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,47.659,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,53.899,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"58.9921838 -9.28833 20.606 12.7178\" width=\"20.606pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,59.042,0)\"><use xlink:href=\"#g113-46\"></use></g><g transform=\"matrix(.013,0,0,-0.013,64.185,0)\"><use xlink:href=\"#g113-46\"></use></g><g transform=\"matrix(.013,0,0,-0.013,69.328,0)\"><use xlink:href=\"#g113-46\"></use></g><g transform=\"matrix(.013,0,0,-0.013,76.684,0)\"><use xlink:href=\"#g113-47\"></use></g></svg><span></span><svg height=\"12.7178pt\" style=\"vertical-align:-3.42947pt\" version=\"1.1\" viewbox=\"79.5981838 -9.28833 4.794 12.7178\" width=\"4.794pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,79.648,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> are considered. The operators <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 43.0414 14.8173\" width=\"43.0414pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,14.556,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.003,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,27.355,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,31.853,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,38.328,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 37.4604 14.8173\" width=\"37.4604pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.422,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.774,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,26.272,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.747,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> satisfy <span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 76.507 14.8173\" width=\"76.507pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.422,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,17.92,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,26.916,3.132)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,32.476,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,36.922,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,45.275,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,49.773,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,56.248,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,60.746,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,68.876,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"80.08818380000001 -9.28833 76.507 14.8173\" width=\"76.507pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,80.138,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,89.135,3.132)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,94.695,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,99.141,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,103.639,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,112.635,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,117.061,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,125.413,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,129.911,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,136.386,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,140.884,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,149.014,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"160.22718379999998 -9.28833 24.429 14.8173\" width=\"24.429pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,160.277,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,168.629,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,173.127,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,179.602,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> and <span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 34.037 14.8173\" width=\"34.037pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,4.498,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,13.494,3.132)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,19.054,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,26.406,0)\"></path></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"36.893183799999996 -9.28833 53.006 14.8173\" width=\"53.006pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,36.943,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,45.939,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,50.364,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,54.862,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,63.215,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,67.713,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,74.188,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,82.318,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"93.5301838 -9.28833 28.457 14.8173\" width=\"28.457pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,93.58,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,98.078,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,107.075,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,114.406,0)\"><use xlink:href=\"#g113-43\"></use></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"124.8921838 -9.28833 58.587 14.8173\" width=\"58.587pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,124.942,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,133.938,3.132)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,139.498,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,143.945,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,148.443,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,156.795,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,161.293,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,167.768,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,175.898,0)\"><use xlink:href=\"#g117-34\"></use></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"187.1111838 -9.28833 23.387 14.8173\" width=\"23.387pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,187.161,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,191.659,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,202.917,0)\"><use xlink:href=\"#g113-43\"></use></g></svg><span></span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"213.4031838 -9.28833 29.071 14.8173\" width=\"29.071pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,213.453,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,221.805,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,226.303,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,230.801,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,237.276,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> for the convolution <svg height=\"6.01072pt\" style=\"vertical-align:-0.04980993pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 7.75925 6.01072\" width=\"7.75925pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-43\"></use></g></svg> of <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 43.0414 14.8173\" width=\"43.0414pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,14.556,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.003,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,27.355,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,31.853,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,38.328,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and <span><svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 40.436 14.8173\" width=\"40.436pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.422,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.774,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,26.272,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.747,0)\"><use xlink:href=\"#g113-42\"></use></g><g transform=\"matrix(.013,0,0,-0.013,37.245,0)\"><use xlink:href=\"#g113-47\"></use></g></svg><span></span></span> In the present paper, the dominants for both operators <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 43.0414 14.8173\" width=\"43.0414pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,14.556,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.003,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,27.355,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,31.853,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,38.328,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 37.4604 14.8173\" width=\"37.4604pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.422,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.774,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,26.272,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.747,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and subordinations for <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 43.0414 14.8173\" width=\"43.0414pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g54-33\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,14.556,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,19.003,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,27.355,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,31.853,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,38.328,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> and <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 37.4604 14.8173\" width=\"37.4604pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.422,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.774,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,26.272,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.747,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> are discussed. Also, new subclass <span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 38.788 14.7625\" width=\"38.788pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,11.856,3.132)\"><use xlink:href=\"#g50-113\"></use></g><g transform=\"matrix(.013,0,0,-0.013,17.807,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,22.305,0)\"></path></g><g transform=\"matrix(.0091,0,0,-0.0091,27.973,3.132)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,35.824,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"40.9171838 -9.28833 9.687 14.7625\" width=\"9.687pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,40.967,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,47.69,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"52.783183799999996 -9.28833 9.974 14.7625\" width=\"9.974pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,52.833,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,59.843,0)\"></path></g></svg><span></span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"64.93618380000001 -9.28833 13.221 14.7625\" width=\"13.221pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,64.986,0)\"></path></g><g transform=\"matrix(.013,0,0,-0.013,75.243,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"80.3361838 -9.28833 10.347 14.7625\" width=\"10.347pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,80.386,0)\"><use xlink:href=\"#g113-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,85.886,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> concerning with <svg height=\"6.1673pt\" style=\"vertical-align:-0.2063904pt\" version=\"1.1\" viewbox=\"-0.0498162 -5.96091 10.3951 6.1673\" width=\"10.3951pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g113-110\"></use></g></svg> different boundary points is defined and discussed. Moreover, some interesting problems of <span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 38.788 14.7625\" width=\"38.788pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-21\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,11.856,3.132)\"><use xlink:href=\"#g50-113\"></use></g><g transform=\"matrix(.013,0,0,-0.013,17.807,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,22.305,0)\"><use xlink:href=\"#g113-225\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,27.973,3.132)\"><use xlink:href=\"#g50-110\"></use></g><g transform=\"matrix(.013,0,0,-0.013,35.824,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"40.9171838 -9.28833 9.687 14.7625\" width=\"9.687pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,40.967,0)\"><use xlink:href=\"#g113-226\"></use></g><g transform=\"matrix(.013,0,0,-0.013,47.69,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"52.783183799999996 -9.28833 9.974 14.7625\" width=\"9.974pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,52.833,0)\"><use xlink:href=\"#g113-239\"></use></g><g transform=\"matrix(.013,0,0,-0.013,59.843,0)\"><use xlink:href=\"#g113-60\"></use></g></svg><span></span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"64.93618380000001 -9.28833 13.221 14.7625\" width=\"13.221pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,64.986,0)\"><use xlink:href=\"#g113-110\"></use></g><g transform=\"matrix(.013,0,0,-0.013,75.243,0)\"><use xlink:href=\"#g113-45\"></use></g></svg><span></span><svg height=\"14.7625pt\" style=\"vertical-align:-5.47417pt\" version=\"1.1\" viewbox=\"80.3361838 -9.28833 10.347 14.7625\" width=\"10.347pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,80.386,0)\"><use xlink:href=\"#g113-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,85.886,0)\"><use xlink:href=\"#g113-42\"></use></g></svg></span> associated with <svg height=\"14.8173pt\" style=\"vertical-align:-5.52897pt\" version=\"1.1\" viewbox=\"-0.0498162 -9.28833 37.4604 14.8173\" width=\"37.4604pt\" xmlns=\"http://www.w3.org/2000/svg\" xmlns:xlink=\"http://www.w3.org/1999/xlink\"><g transform=\"matrix(.013,0,0,-0.013,0,0)\"><use xlink:href=\"#g198-16\"></use></g><g transform=\"matrix(.0091,0,0,-0.0091,8.996,3.132)\"><use xlink:href=\"#g50-107\"></use></g><g transform=\"matrix(.013,0,0,-0.013,13.422,0)\"><use xlink:href=\"#g113-103\"></use></g><g transform=\"matrix(.013,0,0,-0.013,21.774,0)\"><use xlink:href=\"#g113-41\"></use></g><g transform=\"matrix(.013,0,0,-0.013,26.272,0)\"><use xlink:href=\"#g113-123\"></use></g><g transform=\"matrix(.013,0,0,-0.013,32.747,0)\"><use xlink:href=\"#g113-42\"></use></g></svg> are obtained. Furthermore, some interesting examples for our results are considered.","PeriodicalId":15840,"journal":{"name":"Journal of Function Spaces","volume":null,"pages":null},"PeriodicalIF":1.9000,"publicationDate":"2024-01-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"New Integral Operator for Analytic Functions\",\"authors\":\"H. Özlem Güney, Shigeyoshi Owa, Adel A. Attiya\",\"doi\":\"10.1155/2024/5295531\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"Let <svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 31.9134 14.7625\\\" width=\\\"31.9134pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,10.244,3.132)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,16.195,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,20.693,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,27.219,0)\\\"></path></g></svg> be the class of functions <svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 24.0049 12.7178\\\" width=\\\"24.0049pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,8.352,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,12.85,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,19.325,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> given by <span><svg height=\\\"17.0656pt\\\" style=\\\"vertical-align:-5.474199pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -11.5914 35.086 17.0656\\\" width=\\\"35.086pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,8.352,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,12.85,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,19.325,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,27.455,0)\\\"></path></g></svg><span></span><svg height=\\\"17.0656pt\\\" style=\\\"vertical-align:-5.474199pt\\\" version=\\\"1.1\\\" viewbox=\\\"38.6681838 -11.5914 22.963 17.0656\\\" width=\\\"22.963pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,38.718,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,45.193,-5.741)\\\"><use xlink:href=\\\"#g50-113\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,54.05,0)\\\"></path></g></svg><span></span><svg height=\\\"17.0656pt\\\" style=\\\"vertical-align:-5.474199pt\\\" version=\\\"1.1\\\" viewbox=\\\"64.5361838 -11.5914 55.423 17.0656\\\" width=\\\"55.423pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,64.586,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,70.579,3.132)\\\"><use xlink:href=\\\"#g50-113\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,76.013,3.132)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,81.573,3.132)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,86.788,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,93.263,-5.741)\\\"><use xlink:href=\\\"#g50-113\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,98.697,-5.741)\\\"><use xlink:href=\\\"#g54-36\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,104.257,-5.741)\\\"><use xlink:href=\\\"#g50-111\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,112.378,0)\\\"><use xlink:href=\\\"#g117-36\\\"></use></g></svg><span></span><svg height=\\\"17.0656pt\\\" style=\\\"vertical-align:-5.474199pt\\\" version=\\\"1.1\\\" viewbox=\\\"122.8641838 -11.5914 75.481 17.0656\\\" width=\\\"75.481pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,122.914,0)\\\"><use xlink:href=\\\"#g113-98\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,128.907,3.132)\\\"><use xlink:href=\\\"#g50-113\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,134.341,3.132)\\\"><use xlink:href=\\\"#g54-36\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,139.901,3.132)\\\"><use xlink:href=\\\"#g50-111\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,144.56,3.132)\\\"><use xlink:href=\\\"#g54-36\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,150.12,3.132)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,155.145,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,161.62,-5.741)\\\"><use xlink:href=\\\"#g50-113\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,167.054,-5.741)\\\"><use xlink:href=\\\"#g54-36\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,172.614,-5.741)\\\"><use xlink:href=\\\"#g50-111\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,177.273,-5.741)\\\"><use xlink:href=\\\"#g54-36\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,182.833,-5.741)\\\"><use xlink:href=\\\"#g50-50\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,190.764,0)\\\"><use xlink:href=\\\"#g117-36\\\"></use></g></svg><span></span><svg height=\\\"17.0656pt\\\" style=\\\"vertical-align:-5.474199pt\\\" version=\\\"1.1\\\" viewbox=\\\"201.2501838 -11.5914 15.873 17.0656\\\" width=\\\"15.873pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,201.3,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,206.443,0)\\\"><use xlink:href=\\\"#g113-46\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,211.586,0)\\\"><use xlink:href=\\\"#g113-46\\\"></use></g></svg></span> which are analytic in the open unit disk <span><svg height=\\\"8.92059pt\\\" style=\\\"vertical-align:-0.2325001pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -8.68809 12.183 8.92059\\\" width=\\\"12.183pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,9.074,0)\\\"></path></g></svg><span></span></span> For <span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 34.319 14.7625\\\" width=\\\"34.319pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,8.352,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,12.85,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,19.325,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,27.455,0)\\\"></path></g></svg><span></span><span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"37.9011838 -9.28833 32.021 14.7625\\\" width=\\\"32.021pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,37.951,0)\\\"><use xlink:href=\\\"#g113-66\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,48.195,3.132)\\\"><use xlink:href=\\\"#g50-113\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,54.146,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,58.644,0)\\\"><use xlink:href=\\\"#g113-111\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,65.17,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg>,</span></span> new integral operators <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 43.0414 14.8173\\\" width=\\\"43.0414pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,14.556,3.132)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,19.003,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,27.355,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,31.853,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,38.328,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> and <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 37.4604 14.8173\\\" width=\\\"37.4604pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.422,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,21.774,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,26.272,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,32.747,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> <span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 21.261 12.7178\\\" width=\\\"21.261pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,4.498,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,13.63,0)\\\"><use xlink:href=\\\"#g117-34\\\"></use></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"24.843183800000002 -9.28833 9.204 12.7178\\\" width=\\\"9.204pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,24.893,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,31.133,0)\\\"></path></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"36.2261838 -9.28833 9.204 12.7178\\\" width=\\\"9.204pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,36.276,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,42.516,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"47.6091838 -9.28833 9.204 12.7178\\\" width=\\\"9.204pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,47.659,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,53.899,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"58.9921838 -9.28833 20.606 12.7178\\\" width=\\\"20.606pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,59.042,0)\\\"><use xlink:href=\\\"#g113-46\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,64.185,0)\\\"><use xlink:href=\\\"#g113-46\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,69.328,0)\\\"><use xlink:href=\\\"#g113-46\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,76.684,0)\\\"><use xlink:href=\\\"#g113-47\\\"></use></g></svg><span></span><svg height=\\\"12.7178pt\\\" style=\\\"vertical-align:-3.42947pt\\\" version=\\\"1.1\\\" viewbox=\\\"79.5981838 -9.28833 4.794 12.7178\\\" width=\\\"4.794pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,79.648,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> are considered. The operators <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 43.0414 14.8173\\\" width=\\\"43.0414pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g54-33\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,14.556,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,19.003,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,27.355,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,31.853,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,38.328,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> and <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 37.4604 14.8173\\\" width=\\\"37.4604pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.422,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,21.774,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,26.272,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,32.747,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> satisfy <span><svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 76.507 14.8173\\\" width=\\\"76.507pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.422,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,17.92,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,26.916,3.132)\\\"><use xlink:href=\\\"#g54-33\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,32.476,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,36.922,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,45.275,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,49.773,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,56.248,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,60.746,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,68.876,0)\\\"><use xlink:href=\\\"#g117-34\\\"></use></g></svg><span></span><svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"80.08818380000001 -9.28833 76.507 14.8173\\\" width=\\\"76.507pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,80.138,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,89.135,3.132)\\\"><use xlink:href=\\\"#g54-33\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,94.695,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,99.141,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,103.639,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,112.635,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,117.061,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,125.413,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,129.911,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,136.386,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,140.884,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,149.014,0)\\\"><use xlink:href=\\\"#g117-34\\\"></use></g></svg><span></span><svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"160.22718379999998 -9.28833 24.429 14.8173\\\" width=\\\"24.429pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,160.277,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,168.629,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,173.127,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,179.602,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> and <span><svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 34.037 14.8173\\\" width=\\\"34.037pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,4.498,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g 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transform=\\\"matrix(.013,0,0,-0.013,161.293,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,167.768,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,175.898,0)\\\"><use xlink:href=\\\"#g117-34\\\"></use></g></svg><span></span><svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"187.1111838 -9.28833 23.387 14.8173\\\" width=\\\"23.387pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,187.161,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,191.659,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,202.917,0)\\\"><use xlink:href=\\\"#g113-43\\\"></use></g></svg><span></span><svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"213.4031838 -9.28833 29.071 14.8173\\\" width=\\\"29.071pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,213.453,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,221.805,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,226.303,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,230.801,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,237.276,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> for the convolution <svg height=\\\"6.01072pt\\\" style=\\\"vertical-align:-0.04980993pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -5.96091 7.75925 6.01072\\\" width=\\\"7.75925pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-43\\\"></use></g></svg> of <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 43.0414 14.8173\\\" width=\\\"43.0414pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g54-33\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,14.556,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,19.003,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,27.355,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,31.853,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,38.328,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> and <span><svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 40.436 14.8173\\\" width=\\\"40.436pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.422,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,21.774,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,26.272,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,32.747,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,37.245,0)\\\"><use xlink:href=\\\"#g113-47\\\"></use></g></svg><span></span></span> In the present paper, the dominants for both operators <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 43.0414 14.8173\\\" width=\\\"43.0414pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g54-33\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,14.556,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,19.003,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,27.355,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,31.853,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,38.328,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> and <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 37.4604 14.8173\\\" width=\\\"37.4604pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.422,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,21.774,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,26.272,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,32.747,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> and subordinations for <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 43.0414 14.8173\\\" width=\\\"43.0414pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g54-33\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,14.556,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,19.003,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,27.355,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,31.853,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,38.328,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> and <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 37.4604 14.8173\\\" width=\\\"37.4604pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.422,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,21.774,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,26.272,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,32.747,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> are discussed. Also, new subclass <span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 38.788 14.7625\\\" width=\\\"38.788pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,11.856,3.132)\\\"><use xlink:href=\\\"#g50-113\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,17.807,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,22.305,0)\\\"></path></g><g transform=\\\"matrix(.0091,0,0,-0.0091,27.973,3.132)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,35.824,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"40.9171838 -9.28833 9.687 14.7625\\\" width=\\\"9.687pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,40.967,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,47.69,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"52.783183799999996 -9.28833 9.974 14.7625\\\" width=\\\"9.974pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,52.833,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,59.843,0)\\\"></path></g></svg><span></span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"64.93618380000001 -9.28833 13.221 14.7625\\\" width=\\\"13.221pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,64.986,0)\\\"></path></g><g transform=\\\"matrix(.013,0,0,-0.013,75.243,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"80.3361838 -9.28833 10.347 14.7625\\\" width=\\\"10.347pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,80.386,0)\\\"><use xlink:href=\\\"#g113-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,85.886,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> concerning with <svg height=\\\"6.1673pt\\\" style=\\\"vertical-align:-0.2063904pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -5.96091 10.3951 6.1673\\\" width=\\\"10.3951pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g113-110\\\"></use></g></svg> different boundary points is defined and discussed. Moreover, some interesting problems of <span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 38.788 14.7625\\\" width=\\\"38.788pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-21\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,11.856,3.132)\\\"><use xlink:href=\\\"#g50-113\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,17.807,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,22.305,0)\\\"><use xlink:href=\\\"#g113-225\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,27.973,3.132)\\\"><use xlink:href=\\\"#g50-110\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,35.824,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"40.9171838 -9.28833 9.687 14.7625\\\" width=\\\"9.687pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,40.967,0)\\\"><use xlink:href=\\\"#g113-226\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,47.69,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"52.783183799999996 -9.28833 9.974 14.7625\\\" width=\\\"9.974pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,52.833,0)\\\"><use xlink:href=\\\"#g113-239\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,59.843,0)\\\"><use xlink:href=\\\"#g113-60\\\"></use></g></svg><span></span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"64.93618380000001 -9.28833 13.221 14.7625\\\" width=\\\"13.221pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,64.986,0)\\\"><use xlink:href=\\\"#g113-110\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,75.243,0)\\\"><use xlink:href=\\\"#g113-45\\\"></use></g></svg><span></span><svg height=\\\"14.7625pt\\\" style=\\\"vertical-align:-5.47417pt\\\" version=\\\"1.1\\\" viewbox=\\\"80.3361838 -9.28833 10.347 14.7625\\\" width=\\\"10.347pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,80.386,0)\\\"><use xlink:href=\\\"#g113-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,85.886,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg></span> associated with <svg height=\\\"14.8173pt\\\" style=\\\"vertical-align:-5.52897pt\\\" version=\\\"1.1\\\" viewbox=\\\"-0.0498162 -9.28833 37.4604 14.8173\\\" width=\\\"37.4604pt\\\" xmlns=\\\"http://www.w3.org/2000/svg\\\" xmlns:xlink=\\\"http://www.w3.org/1999/xlink\\\"><g transform=\\\"matrix(.013,0,0,-0.013,0,0)\\\"><use xlink:href=\\\"#g198-16\\\"></use></g><g transform=\\\"matrix(.0091,0,0,-0.0091,8.996,3.132)\\\"><use xlink:href=\\\"#g50-107\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,13.422,0)\\\"><use xlink:href=\\\"#g113-103\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,21.774,0)\\\"><use xlink:href=\\\"#g113-41\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,26.272,0)\\\"><use xlink:href=\\\"#g113-123\\\"></use></g><g transform=\\\"matrix(.013,0,0,-0.013,32.747,0)\\\"><use xlink:href=\\\"#g113-42\\\"></use></g></svg> are obtained. Furthermore, some interesting examples for our results are considered.\",\"PeriodicalId\":15840,\"journal\":{\"name\":\"Journal of Function Spaces\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.9000,\"publicationDate\":\"2024-01-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Function Spaces\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1155/2024/5295531\",\"RegionNum\":3,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Function Spaces","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1155/2024/5295531","RegionNum":3,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
摘要
对于 ，我们考虑了新的积分算子 和 。在本文中，讨论了运算符 和 的支配性以及 和 的从属性。此外，还定义并讨论了与不同边界点有关的新子类。此外，还得到了与 的相关联的一些有趣问题。此外，本文还考虑了一些与我们的结果相关的有趣例子。本文章由计算机程序翻译，如有差异，请以英文原文为准。
New Integral Operator for Analytic Functions
Let be the class of functions given by which are analytic in the open unit disk For , new integral operators and are considered. The operators and satisfy and for the convolution of and In the present paper, the dominants for both operators and and subordinations for and are discussed. Also, new subclass concerning with different boundary points is defined and discussed. Moreover, some interesting problems of associated with are obtained. Furthermore, some interesting examples for our results are considered.
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来源期刊
Journal of Function Spaces
MATHEMATICS, APPLIEDMATHEMATICS -MATHEMATICS
CiteScore
4.10
自引率
10.50%
发文量
451
审稿时长
15 weeks
期刊介绍：
Journal of Function Spaces (formerly titled Journal of Function Spaces and Applications) publishes papers on all aspects of function spaces, functional analysis, and their employment across other mathematical disciplines. As well as original research, Journal of Function Spaces also publishes focused review articles that assess the state of the art, and identify upcoming challenges and promising solutions for the community.
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