On a weighted Hermite-Hadamard inequality involving convex functional arguments

TL;DR

This paper explores a weighted Hermite-Hadamard inequality for convex functionals, refining existing inequalities and introducing new weighted means with related properties.

Contribution

It presents a new weighted Hermite-Hadamard inequality for convex functionals, refining and reversing known inequalities and defining novel weighted means.

Findings

Refined Hermite-Hadamard inequalities for convex functionals

Introduction of new weighted convex functional means

Establishment of properties relating to standard means

Abstract

In this paper, we are interested in investigating a weighted variant of Hermite-Hadamard type inequalities involving convex functionals. The approach undertaken makes it possible to refine and reverse certain inequalities already known in the literature. It also allows us to provide new weighted convex functional means and establish some related properties with respect to some standard means.