On the weighted hermite-hadamard inequality in multiple variables, application for weighted multivariate means (2405.12251v1)

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.