Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions

Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions

In this paper, we define a new function, namely, harmonically α,h−m-convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α,h−m-convex functions via generalized frac...

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Main Authors: Chahn Yong Jung, Muhammad Yussouf, Yu-Ming Chu, Ghulam Farid, Shin Min Kang
Format: Article
Language:English
Published: Hindawi Limited 2020-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2020/8245324
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spelling doaj-8ce0c6a91e8849f4933808c7b1073b432020-11-25T04:02:44ZengHindawi LimitedJournal of Mathematics2314-46292314-47852020-01-01202010.1155/2020/82453248245324Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex FunctionsChahn Yong Jung0Muhammad Yussouf1Yu-Ming Chu2Ghulam Farid3Shin Min Kang4Department of Business Administration, Gyeongsang National University, Jinju 52828, Republic of KoreaDepartment of Mathematics, University of Sargodha, Sargodha, PakistanDepartment of Mathematics, Huzhou University, Huzhou 313000, ChinaDepartment of Mathematics, COMSATS University Islamabad, Attock, PakistanCenter for General Education, China Medical University, Taichung 40402, TaiwanIn this paper, we define a new function, namely, harmonically α,h−m-convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α,h−m-convex functions via generalized fractional integral operators are proved. From presented results, a series of fractional integral inequalities can be obtained for harmonically convex, harmonically h−m-convex, harmonically α,m-convex, and related functions and for already known fractional integral operators.http://dx.doi.org/10.1155/2020/8245324
collection DOAJ
language English
format Article
sources DOAJ
author Chahn Yong Jung
Muhammad Yussouf
Yu-Ming Chu
Ghulam Farid
Shin Min Kang
spellingShingle Chahn Yong Jung
Muhammad Yussouf
Yu-Ming Chu
Ghulam Farid
Shin Min Kang
Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions
Journal of Mathematics
author_facet Chahn Yong Jung
Muhammad Yussouf
Yu-Ming Chu
Ghulam Farid
Shin Min Kang
author_sort Chahn Yong Jung
title Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions
title_short Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions
title_full Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions
title_fullStr Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions
title_full_unstemmed Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions
title_sort generalized fractional hadamard and fejér–hadamard inequalities for generalized harmonically convex functions
publisher Hindawi Limited
series Journal of Mathematics
issn 2314-4629
2314-4785
publishDate 2020-01-01
description In this paper, we define a new function, namely, harmonically α,h−m-convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejér–Hadamard fractional integral inequalities for harmonically α,h−m-convex functions via generalized fractional integral operators are proved. From presented results, a series of fractional integral inequalities can be obtained for harmonically convex, harmonically h−m-convex, harmonically α,m-convex, and related functions and for already known fractional integral operators.
url http://dx.doi.org/10.1155/2020/8245324
work_keys_str_mv AT chahnyongjung generalizedfractionalhadamardandfejerhadamardinequalitiesforgeneralizedharmonicallyconvexfunctions
AT muhammadyussouf generalizedfractionalhadamardandfejerhadamardinequalitiesforgeneralizedharmonicallyconvexfunctions
AT yumingchu generalizedfractionalhadamardandfejerhadamardinequalitiesforgeneralizedharmonicallyconvexfunctions
AT ghulamfarid generalizedfractionalhadamardandfejerhadamardinequalitiesforgeneralizedharmonicallyconvexfunctions
AT shinminkang generalizedfractionalhadamardandfejerhadamardinequalitiesforgeneralizedharmonicallyconvexfunctions
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