A Comprehensive Study of Refined Hermite-Hadamard Inequalities and Their Applications

Abstract

In this article, we explore a novel class of Hermite-Hadamard inequalities via exponential type convexity. To establish the main results, we primarily use Holder’s inequality, the power mean inequality and some generalized associated inequalities. These inequalities have strong applicability in inequalities and optimization theory. Moreover, we compare the main findings to demonstrate that the Holder-Iscan inequality can yield more refined results than Holder’s inequality and the improved power mean inequality can offer better refinements of Hermite-Hadamard inequalities than the power mean inequality. Additionally, we provide some applications for generalized means.