Generalized Fractional Hadamard and Fejér–Hadamard Inequalities for Generalized Harmonically Convex Functions. (4th November 2020)

• Record Type: Journal Article
• Authors: Jung, Chahn Yong; Yussouf, Muhammad; Chu, Yu-Ming; Farid, Ghulam; Kang, Shin Min
• Other Names: Ueki Sei Ichiro Academic Editor.
• Is Part Of: Journal of mathematics. Volume 2020(2020)
• Publication Date: 2020-11-04
• Subjects: Mathematics -- Periodicals; Mathematics; Periodicals; 510
• DOI: 10.1155/2020/8245324
• Languages: English
• ISSNs: 2314-4629

Abstract

Abstract : 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.