On new general integral inequalities for h- convex functions

TL;DR

This paper introduces new integral inequalities for h-convex functions, providing refined estimates for classical numerical integration formulas and exploring applications to special means of real numbers.

Contribution

It presents novel bounds for the remainder terms of midpoint, trapezoid, and Simpson formulas specifically for h-convex functions, extending existing inequalities.

Findings

Derived new bounds for numerical integration formulas

Extended inequalities to h-convex functions and special classes

Applied results to inequalities involving special means

Abstract

In this paper, we derive new estimates for the remainder term of the midpoint, trapezoid, and Simpson formulae for functions whose derivatives in absolute value at certain power are h-convex and we point out the results for some special classes of functions. Some applications to special means of real numbers are also given.