( p , h )-Convex Functions Associated with Hadamard and Fejér-Hadamard Inequalities via k -Fractional Integral Operators

Abstract

In this article, generalized versions of the $k$ -fractional Hadamard and Fejér-Hadamard inequalities are constructed. To obtain the generalized versions of these inequalities, $k$ -fractional integral operators including the well-known Mittag-Leffler function are utilized. The class of ( $p,h$ )-convex functions for Hadamard-type inequalities give the generalizations of results which have been proved in literature for $p$ -convex, $h$ -convex, and several functions deducible from these two classes.