HERMITE–HADAMARD–FEJÉR-TYPE INEQUALITIES VIA KATUGAMPOLA FRACTIONAL INTEGRALS FOR S-CONVEX FUNCTIONS IN THE SECOND SENSE

Abstract

The Hermite–Hadamard–Fejér-type inequality is a powerful tool for studying lower and upper estimations for the integral average of convex function. In this paper, we adopt Hölder’s inequality to establish Hermite–Hadamard–Fejér-type inequalities via Katugampola fractional integrals for the function [Formula: see text], where [Formula: see text] is an s-convex function on [Formula: see text] and [Formula: see text] is symmetric with respect to [Formula: see text]. Our results are generalizations of some earlier results. At the end of the paper, illustrative examples about Hermite–Hadamard–Fejér-type inequalities are given to support our results.