New Fractional Hermite–Hadamard–Mercer Inequalities for Harmonically Convex Function. (25th October 2021)

• Record Type: Journal Article
• Authors: Butt, Saad Ihsan; Yousaf, Saba; Asghar, Atifa; Khan, Khuram Ali; Moradi, Hamid Reza
• Other Names: Tang Huo Academic Editor.
• Is Part Of: Journal of function spaces. Volume 2021(2021)
• Publication Date: 2021-10-25
• Subjects: Function spaces -- Periodicals; 515.7305
• DOI: 10.1155/2021/5868326
• Languages: English
• ISSNs: 2314-8896

Abstract

Abstract : 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.