Improvements of the weighted Hermite-Hadamard inequality and applications to mean inequality

TL;DR

This paper enhances the weighted Hermite-Hadamard inequality, providing improved bounds for weighted means and extending known results with new inequalities and modifications.

Contribution

It introduces new characterizations and modifications of the weighted Hermite-Hadamard inequality, leading to improved inequalities for weighted means.

Findings

New inequalities for weighted means derived

Extensions of existing Hermite-Hadamard inequalities

Modified inequalities with broader applicability

Abstract

This paper aims to characterize the function appearing in the weighted Hermite-Hadamard inequality. We provide improved inequalities for the weighted means as applications of the obtained results. Modifications of the weighted Hermite-Hadamard inequality are also presented. Our results contain some exciting inequalities and extensions of the known results.