Refinement of the right-hand side of Hermite-Hadamard inequality for simplices

TL;DR

This paper presents a new refinement of the Hermite-Hadamard inequality specifically for simplices, utilizing average values over faces and barycenters to improve the inequality's bounds.

Contribution

It introduces a novel refinement of the Hermite-Hadamard inequality for simplices based on face averages and barycenter evaluations, advancing convex analysis techniques.

Findings

Refined inequality bounds for convex functions on simplices

Utilization of face averages and barycenters in the inequality

Enhanced understanding of convex function behavior on simplices

Abstract

We establish a new refinement of the right-hand side of the Hermite-Hadamard inequality for simplices, based on the average values of a convex function over the faces of a simplex and over the values at their barycenters.