New fractional Hermite-Hadamard-Mercer inequalities for harmonically convex function
type: Item
instance of: scholarly article
title: New fractional Hermite-Hadamard-Mercer inequalities for harmonically convex function
zbMATH Open document ID: 1484.26055
DOI: 10.1155/2021/5868326
author: S. I. Butt
author: Saba Yousaf
author: Atifa Asghar
author: Khuram Ali Khan
author: Hamid Reza Moradi
published in: Journal of Function Spaces
publication date: 2021-12-16T00:00:00Z
review text: Summary: In 2003, \textit{A. McD. Mercer} [JIPAM, J. Inequal. Pure Appl. Math. 4, No. 4, Paper No. 73, 2 p. (2003; Zbl 1048.26016)] 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.
Mathematics Subject Classification ID: 26D15
Mathematics Subject Classification ID: 26A51
zbMATH DE Number: 7446735
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2021/5868326
OpenAlex ID: W3211008961
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description: scientific article; zbMATH DE number 7446735