New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional in...

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Autores principales:	Saad Ihsan Butt, Saba Yousaf, Atifa Asghar, Khuram Ali Khan, Hamid Reza Moradi
Formato:	article
Lenguaje:	EN
Publicado:	Hindawi Limited 2021
Materias:	Mathematics QA1-939
Acceso en línea:	https://doaj.org/article/8fe6f72507394b70a09af4bead2bcb05
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spelling	oai:doaj.org-article:8fe6f72507394b70a09af4bead2bcb052021-11-08T02:35:22ZNew Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function2314-888810.1155/2021/5868326https://doaj.org/article/8fe6f72507394b70a09af4bead2bcb052021-01-01T00:00:00Zhttp://dx.doi.org/10.1155/2021/5868326https://doaj.org/toc/2314-8888In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional integrals. As a result, we introduce several related fractional inequalities connected with the right and left differences of obtained new inequalities for differentiable harmonically convex mappings. As an application viewpoint, new estimates regarding hypergeometric functions and special means of real numbers are exemplified to determine the pertinence and validity of the suggested scheme. Our results presented here provide extensions of others given in the literature. The results proved in this paper may stimulate further research in this fascinating area.Saad Ihsan ButtSaba YousafAtifa AsgharKhuram Ali KhanHamid Reza MoradiHindawi LimitedarticleMathematicsQA1-939ENJournal of Function Spaces, Vol 2021 (2021)
institution	DOAJ
collection	DOAJ
language	EN
topic	Mathematics QA1-939
spellingShingle	Mathematics QA1-939 Saad Ihsan Butt Saba Yousaf Atifa Asghar Khuram Ali Khan Hamid Reza Moradi New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function
description	In 2003, Mercer presented an interesting variation of Jensen’s inequality called Jensen–Mercer inequality for convex function. In the present paper, by employing harmonically convex function, we introduce analogous versions of Hermite–Hadamard inequalities of the Jensen–Mercer type via fractional integrals. As a result, we introduce several related fractional inequalities connected with the right and left differences of obtained new inequalities for differentiable harmonically convex mappings. As an application viewpoint, new estimates regarding hypergeometric functions and special means of real numbers are exemplified to determine the pertinence and validity of the suggested scheme. Our results presented here provide extensions of others given in the literature. The results proved in this paper may stimulate further research in this fascinating area.
format	article
author	Saad Ihsan Butt Saba Yousaf Atifa Asghar Khuram Ali Khan Hamid Reza Moradi
author_facet	Saad Ihsan Butt Saba Yousaf Atifa Asghar Khuram Ali Khan Hamid Reza Moradi
author_sort	Saad Ihsan Butt
title	New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function
title_short	New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function
title_full	New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function
title_fullStr	New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function
title_full_unstemmed	New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function
title_sort	new fractional hermite–hadamard–mercer inequalities for harmonically convex function
publisher	Hindawi Limited
publishDate	2021
url	https://doaj.org/article/8fe6f72507394b70a09af4bead2bcb05
work_keys_str_mv	AT saadihsanbutt newfractionalhermitehadamardmercerinequalitiesforharmonicallyconvexfunction AT sabayousaf newfractionalhermitehadamardmercerinequalitiesforharmonicallyconvexfunction AT atifaasghar newfractionalhermitehadamardmercerinequalitiesforharmonicallyconvexfunction AT khuramalikhan newfractionalhermitehadamardmercerinequalitiesforharmonicallyconvexfunction AT hamidrezamoradi newfractionalhermitehadamardmercerinequalitiesforharmonicallyconvexfunction
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New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function

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