On Iyengar-Type Inequalities via Quasi-Convexity and Quasi-Concavity

TL;DR

This paper presents new bounds for Iyengar-type inequalities involving quasi-convex and quasi-concave functions, improves existing estimations, and provides applications to special means and error bounds for trapezoidal rule.

Contribution

It introduces novel estimations of Iyengar-type inequalities involving quasi-convexity and quasi-concavity, enhancing previous results and including error bounds for numerical integration.

Findings

New inequalities involving quasi-convex and quasi-concave functions.

Improved estimations over previous bounds.

Applications to special means and trapezoidal rule error bounds.

Abstract

In this paper, we obtain some new estimations of Iyengar-type inequality in which quasi-convex(quasi-concave) functions are involved. These estimations are improvements of some recently obtained estimations. Some error estimations for the trapezoidal formula are given. Applications for special means are also provided.