On Hadamard Type Inequalities Involving Several Kind of Convexity

TL;DR

This paper extends Hadamard inequalities to various convex functions including log-convex, m-convex, and (alpha,m)-convex, providing new bounds and generalizations in the field of convex analysis.

Contribution

It introduces new Hadamard type inequalities for multiple convexity classes, expanding the scope of existing inequalities and their applications.

Findings

Extended inequalities for log-convex functions

Derived new bounds for m-convex functions

Generalized inequalities for (alpha,m)-convex functions

Abstract

In this paper, we not only give the extensions of the results given in [7] by Gill et al. for log-convex functions, but also obtain some new Hadamard type inequalities for log-convex, m-convex and (alpha,m)-convex functions.