Hermite-Hadamard-type inequalities in the approximate integration

TL;DR

This paper extends Hermite-Hadamard inequalities to simplices and applies these results to derive error bounds for operators used in approximate integration, enhancing the theoretical understanding of numerical integration methods.

Contribution

It introduces a new extension of Hermite-Hadamard inequalities for simplices and utilizes it to establish error bounds for approximate integration operators.

Findings

Extended Hermite-Hadamard inequalities to simplices.

Derived new error bounds for approximate integration operators.

Improved theoretical framework for numerical integration accuracy.

Abstract

We give a slight extension of the Hermite-Hadamard inequality on simplices and we use it to establish error bounds of the operators connected with the approximate integration.