New estimates on generalization of some integral inequalities for quasi-convex functions and their applications

TL;DR

This paper presents new bounds for classical integral inequalities applied to quasi-convex functions, enhancing understanding of their approximation errors and applications to special means.

Contribution

It introduces novel estimates for the remainder terms of midpoint, trapezoid, and Simpson formulas specifically for quasi-convex functions, expanding existing inequality theory.

Findings

Derived new bounds for integral approximation formulas

Applied results to inequalities involving special means

Enhanced understanding of quasi-convex function behavior

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 quasi-convex. Some applications to special means of real numbers are also given.