On Hermite Hadamard inequalities for product of two log-{\varphi}-convex functions

TL;DR

This paper introduces log-{ ext{ extphi}}-convex functions, explores their properties, and extends Hermite-Hadamard inequalities to the product of such functions, contributing to convex analysis and inequality theory.

Contribution

It defines log-{ ext{ extphi}}-convex functions and establishes Hermite-Hadamard inequalities for their products, advancing the understanding of convexity-related inequalities.

Findings

Properties and representations of log-{ ext{ extphi}}-convex functions

Hermite-Hadamard inequalities for the product of log-{ ext{ extphi}}-convex functions

Extension of classical inequalities to new function classes

Abstract

In this paper, we introduce the notion of log-{\varphi}-convex functions and present some properties and representation of such functions. We obtain some results of the Hermite Hadamard inequalities for product log-{\varphi}-convex functions.