Hermite–Hadamard-type inequalities via different convexities with applications

Abstract

In this paper, we explore a class of Hermite–Hadamard integral inequalities for convex and m-convex functions. The Hölder inequality is used to create this class, which has a wide range of applications in optimization theory. Some trapezoid-type inequalities and midpoint error estimates are investigated. Inequalities for several q-special functions are highlighted. As particular cases, we have included several previous results.

A Study of Some New Hermite–Hadamard Inequalities via Specific Convex Functions with Applications

“…Additionally, a number of mathematicians have developed Hermite-Hadmard-type inequality inequalities for differentiable convex mappings [14], s-convex functions [15], m-convex mappings [16], and Green's functions [17]. Numerous scholars have presented applications for fractional operators, see, for example [18,19]. Kadakal and Iscan gave a new description for the exponential-type convex function [20].…”