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

摘要

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.