{"title":"指数广义(m,ω,h_1,h_2)-前倒凸函数的分数不等式及其应用","authors":"A. Kashuri, M. Kunt","doi":"10.7153/fdc-2020-10-05","DOIUrl":null,"url":null,"abstract":". The aim of this paper is to introduce a new extension of preinvexity called expo- nentially generalized ( m , ω , h 1 , h 2 ) –preinvexity. Some new integral inequalities of Hermite– Hadamard type for exponentially generalized ( m , ω , h 1 , h 2 ) –preinvex functions via Riemann– Liouville fractional integral are established. We show that the class of exponentially generalized ( m , ω , h 1 , h 2 ) –preinvex functions includes several other classes of preinvex functions. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.","PeriodicalId":135809,"journal":{"name":"Fractional Differential Calculus","volume":"1 1","pages":"0"},"PeriodicalIF":0.0000,"publicationDate":"1900-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Fractional inequalities for exponentially generalized (m,ω,h_1,h_2)-preinvex functions with applications\",\"authors\":\"A. Kashuri, M. Kunt\",\"doi\":\"10.7153/fdc-2020-10-05\",\"DOIUrl\":null,\"url\":null,\"abstract\":\". The aim of this paper is to introduce a new extension of preinvexity called expo- nentially generalized ( m , ω , h 1 , h 2 ) –preinvexity. Some new integral inequalities of Hermite– Hadamard type for exponentially generalized ( m , ω , h 1 , h 2 ) –preinvex functions via Riemann– Liouville fractional integral are established. We show that the class of exponentially generalized ( m , ω , h 1 , h 2 ) –preinvex functions includes several other classes of preinvex functions. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.\",\"PeriodicalId\":135809,\"journal\":{\"name\":\"Fractional Differential Calculus\",\"volume\":\"1 1\",\"pages\":\"0\"},\"PeriodicalIF\":0.0000,\"publicationDate\":\"1900-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Fractional Differential Calculus\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.7153/fdc-2020-10-05\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Fractional Differential Calculus","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.7153/fdc-2020-10-05","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
引用次数: 0
摘要
. 本文的目的是引入先验性的一个新的推广,称为expo-本质广义(m, ω, h 1, h 2) -先验性。利用Riemann - Liouville分数积分建立了指数广义(m, ω, h 1, h 2) -预逆函数的Hermite - Hadamard型积分不等式。我们证明了一类指数广义(m, ω, h 1, h 2) -预凸函数包含了其他几类预凸函数。最后,对梯形正交公式给出了一些新的误差估计。这一结果可能会激发在纯科学和应用科学不同领域的进一步研究。
Fractional inequalities for exponentially generalized (m,ω,h_1,h_2)-preinvex functions with applications
. The aim of this paper is to introduce a new extension of preinvexity called expo- nentially generalized ( m , ω , h 1 , h 2 ) –preinvexity. Some new integral inequalities of Hermite– Hadamard type for exponentially generalized ( m , ω , h 1 , h 2 ) –preinvex functions via Riemann– Liouville fractional integral are established. We show that the class of exponentially generalized ( m , ω , h 1 , h 2 ) –preinvex functions includes several other classes of preinvex functions. At the end, some new error estimates for trapezoidal quadrature formula are provided as well. This results may stimulate further research in different areas of pure and applied sciences.