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

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.

arXiv comment16 pages