A new variant of weighted Hermite-Hadamard inequalities and applications

TL;DR

This paper introduces a novel variant of Hermite-Hadamard inequalities for operator convex maps, providing refinements of existing inequalities and defining new weighted operator means, with potential applications in operator theory.

Contribution

It presents a new variant of Hermite-Hadamard inequalities for operator convex maps and explores their applications in refining operator inequalities and defining new operator means.

Findings

New Hermite-Hadamard inequality variant for operator convex maps

Refinements of existing operator inequalities

Introduction of new weighted operator means

Abstract

In this article, we focus on establishing a new variant of Hermite-Hadamard type inequalities for operator convex maps using an appropriate probability measure. To underline the usefulness of these inequalities, we investigate some refinements of some well-known operator inequalities, as well as the definition of new weighted operator means.