Generalized Fractional Hadamard and Fejer-Hadamard Inequalities for Generalized Harmonically Convex Functions

Abstract

In this paper, we define a new function, namely, harmonically (a, h - m)-convex function, which unifies various kinds of harmonically convex functions. Generalized versions of the Hadamard and the Fejer-Hadamard fractional integral inequalities for harmonically (alpha, 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 (alpha, m)-convex, and related functions and for already known fractional integral operators.