New Hermite-Hadamard type integral inequalities for convex functions and theirs applications

TL;DR

This paper introduces new Hermite-Hadamard type integral inequalities for convex functions, with applications to special means, error estimates, and inequalities for special functions.

Contribution

It presents novel integral inequalities for convex functions and applies them to derive inequalities for means, error bounds, and special functions.

Findings

New inequalities for convex functions established

Applications to special means and error estimates demonstrated

Inequalities for special and q-special functions derived

Abstract

In this paper, we establish (presumably new type) integral inequalities for convex functions via the Hermite--Hadamard's inequalities. As applications, we apply these new inequalities to construct inequalities involving special means of real numbers, some error estimates for the formula midpoint are given. Finally, new inequalities for some special and $q-$special functions are also pointed out.