On the weighted hermite-hadamard inequality in multiple variables, application for weighted multivariate means

TL;DR

This paper extends the Hermite-Hadamard inequality to multiple variables with weights and introduces new weighted multivariate means, broadening the scope of convex analysis and mean inequalities.

Contribution

It develops a weighted multivariate Hermite-Hadamard inequality and proposes new weighted multivariate means, advancing the theory of convex functions and inequalities.

Findings

Extended Hermite-Hadamard inequality to multiple variables with weights

Introduced new weighted multivariate means

Provided applications to existing bivariate means

Abstract

Recently, the so-called Hermite-Hadamard inequality for (operator) convex functions with one variable has known extensive several developments by virtue of its nice properties and various applications. The fundamental target of this paper is to investigate a weighted variant of Hermite-Hadamard inequality in multiple variables that extends the univariate case. As an application, we introduce some weighted multivariate means extending certain bivariate means known in the literature.