A new generalization of some integral inequalities for ({\alpha},m)-convex functions

TL;DR

This paper introduces new bounds for integral inequalities related to ({},m)-convex functions, enhancing the understanding of approximation errors in numerical integration formulas.

Contribution

It provides novel estimates for the remainder terms of midpoint, trapezoid, and Simpson rules for ({},m)-convex functions, extending existing inequalities.

Findings

Derived new bounds for approximation errors

Extended inequalities to ({},m)-convex functions

Improved accuracy estimates for numerical integration

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.