{"title":"若干类函数的畸变、凹半径和若干其他半径结果","authors":"Bappaditya Bhowmik, Souvik Biswas","doi":"10.1007/s40315-024-00525-8","DOIUrl":null,"url":null,"abstract":"<p>Let <i>S</i>(<i>p</i>) be the class of all meromorphic univalent functions defined in the unit disc <span>\\({\\mathbb D}\\)</span> of the complex plane with a simple pole at <span>\\(z=p\\)</span> and normalized by the conditions <span>\\(f(0)=0\\)</span> and <span>\\(f'(0)=1\\)</span>. In this article, we establish an estimate of the quantity <span>\\(|zf'/f|\\)</span> and obtain the region of variability of the function <span>\\(zf''/f'\\)</span> for <span>\\(z\\in {\\mathbb D}\\)</span>, <span>\\(f\\in S(p)\\)</span>. After that, we define radius of concavity and compute the same for functions in <i>S</i>(<i>p</i>) and for some other well-known classes of functions. We also explore linear combinations of functions belonging to <i>S</i>(<i>p</i>) and some other classes of analytic univalent functions and investigate their radii of univalence, convexity and concavity.</p>","PeriodicalId":49088,"journal":{"name":"Computational Methods and Function Theory","volume":"37 1","pages":""},"PeriodicalIF":0.6000,"publicationDate":"2024-04-12","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Distortion, Radius of Concavity and Several Other Radii Results for Certain Classes of Functions\",\"authors\":\"Bappaditya Bhowmik, Souvik Biswas\",\"doi\":\"10.1007/s40315-024-00525-8\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<p>Let <i>S</i>(<i>p</i>) be the class of all meromorphic univalent functions defined in the unit disc <span>\\\\({\\\\mathbb D}\\\\)</span> of the complex plane with a simple pole at <span>\\\\(z=p\\\\)</span> and normalized by the conditions <span>\\\\(f(0)=0\\\\)</span> and <span>\\\\(f'(0)=1\\\\)</span>. In this article, we establish an estimate of the quantity <span>\\\\(|zf'/f|\\\\)</span> and obtain the region of variability of the function <span>\\\\(zf''/f'\\\\)</span> for <span>\\\\(z\\\\in {\\\\mathbb D}\\\\)</span>, <span>\\\\(f\\\\in S(p)\\\\)</span>. After that, we define radius of concavity and compute the same for functions in <i>S</i>(<i>p</i>) and for some other well-known classes of functions. We also explore linear combinations of functions belonging to <i>S</i>(<i>p</i>) and some other classes of analytic univalent functions and investigate their radii of univalence, convexity and concavity.</p>\",\"PeriodicalId\":49088,\"journal\":{\"name\":\"Computational Methods and Function Theory\",\"volume\":\"37 1\",\"pages\":\"\"},\"PeriodicalIF\":0.6000,\"publicationDate\":\"2024-04-12\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods and Function Theory\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1007/s40315-024-00525-8\",\"RegionNum\":4,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods and Function Theory","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40315-024-00525-8","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
Distortion, Radius of Concavity and Several Other Radii Results for Certain Classes of Functions
Let S(p) be the class of all meromorphic univalent functions defined in the unit disc \({\mathbb D}\) of the complex plane with a simple pole at \(z=p\) and normalized by the conditions \(f(0)=0\) and \(f'(0)=1\). In this article, we establish an estimate of the quantity \(|zf'/f|\) and obtain the region of variability of the function \(zf''/f'\) for \(z\in {\mathbb D}\), \(f\in S(p)\). After that, we define radius of concavity and compute the same for functions in S(p) and for some other well-known classes of functions. We also explore linear combinations of functions belonging to S(p) and some other classes of analytic univalent functions and investigate their radii of univalence, convexity and concavity.
期刊介绍:
CMFT is an international mathematics journal which publishes carefully selected original research papers in complex analysis (in a broad sense), and on applications or computational methods related to complex analysis. Survey articles of high standard and current interest can be considered for publication as well.