On new Hermite-Hadamard-Fejer type inequalities for p-convex functions via fractional integrals

Abstract

In this paper, firstly, new Hermite-Hadamard-Fejer type inequalities for p-convex functions in fractional integral forms are built. Secondly, an integral identity and some Hermite-Hadamard-Fejer type integral inequalities for p-convex functions in fractional integral forms are obtained. Finally, some Hermite-Hadamard and Hermite-Hadamard-Fejer inequalities for convex, harmonically convex and p-convex functions are given. Many results presented here for p-convex functions provide extensions of others given in earlier works for convex, harmonically convex and p-convex functions.

Keywords

• Hermite-Hadamard inequalities, Hermite-Hadamard-Fejer inequalities, fractional integral, convex functions, harmonically convex functions, p-convex functions