Hermite-Hadamard type inequalities for functions whose derivatives are ({\alpha},m)-convex

TL;DR

This paper derives new Hermite-Hadamard type inequalities for functions with derivatives that are ({},m)-convex in absolute value, and applies these results to inequalities involving special means of positive real numbers.

Contribution

It introduces novel Hermite-Hadamard inequalities for ({},m)-convex derivative functions and explores their applications to special means.

Findings

Established new inequalities for ({},m)-convex functions

Extended Hermite-Hadamard inequalities to derivative-based functions

Applied results to inequalities of positive real number means

Abstract

In this paper several inequalities of the right-hand side of Hermite-Hadamard inequality are obtained for the class of functions whose derivatives in absolutely value at certain powers are ({\alpha},m)-convex.Some applications to special means of positive real numbers are also given.