New estimates on generalization of some integral inequalities for (alpha,m)-convex functions

TL;DR

This paper introduces new bounds for classical integral inequalities applied to ({},m)-convex functions, enhancing understanding of their approximation errors.

Contribution

It provides novel estimates for the remainder terms of midpoint, trapezoid, and Simpson formulas specifically for ({},m)-convex functions.

Findings

Derived new bounds for integral inequalities

Applied estimates to ({},m)-convex functions

Improved understanding of approximation errors

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 ({\alpha},m)-convex.