Study on fractional fejÉr-hadamard type inequalities associated with generalized exponentially convexity

作     者：Farid, Ghulam Guran, Liliana Qiang, Xiaoli Chu, Yu-Ming 

作者机构：Department of Mathematics COMSATS University Islamabad Attock Campus Pakistan Department of Pharmaceutical Sciences "Vasile Goldiş" Western University L. Rebreanu Street no. 86 Arad310048 Romania Institute of Computing Science and Technology Guangzhou University Guangzhou510006 China Department of Mathematics Huzhou University Huzhou313000 China Hunan Provincial Key Labo-ratory of Mathematical Modeling and Analysis in Engineering Changsha University of Science & Technology Changsha410114 China 

出 版 物：《UPB Scientific Bulletin, Series A: Applied Mathematics and Physics》 (UPB Sci Bull Ser A)

年 卷 期：2021年第83卷第4期

页      面：159-170页

核心收录：

学科分类：07[理学] 0701[理学-数学] 070101[理学-基础数学] 

基　　金：This work is supported by the National Natural Science Foundation of China (Grant Nos. 11971142  11871202  61673169  11701176  11626101  11601485) 

主　　题：Mathematical operators 

摘      要：In this paper fractional integral inequalities of Fejér-Hadamard type for a generalized notion of convexity are established. A new generalization of convexity named exponentially (α, h − m)-convex function unifies exponentially (h − m)-convex, exponentially (α − m)-convex and exponentially (s, m)-convex functions. By using the generalized fractional integral operators involving Mittag-Leffler function via a monotonically increasing function we have obtained some fractional versions of Fejér-Hadamard inequality for the generalized convexity. The obtained results lead to many inequalities of Fejér-Hadamard and Hadamard type for well-known fractional integral operators and different kinds of convexities. © 2021, Politechnica University of Bucharest. All rights reserved.