On new general integral inequalities for quasi-convex functions and their applications

TL;DR

This paper develops new integral inequalities for quasi-convex functions, providing improved estimates for classical numerical integration formulas and applying these results to special means of real numbers.

Contribution

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

Findings

New bounds for numerical integration remainders for quasi-convex functions

Applications to inequalities involving special means of real numbers

Enhanced understanding of integral inequalities in the context of quasi-convexity

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.