An Inequality of Simpson's type Via Quasi-Convex Mappings with Applications

TL;DR

This paper establishes a new Simpson's type inequality for quasi-convex functions, improving the classical bounds and demonstrating better estimates than recent results, with applications to numerical integration.

Contribution

It introduces a novel Simpson's inequality for quasi-convex functions that enhances existing bounds and applies these results to Simpson's quadrature rule.

Findings

Improved bounds for Simpson's inequality for quasi-convex functions

Demonstrated superiority over recent bounds in the literature

Applied the inequality to numerical integration methods

Abstract

In this paper, an inequality of Simpson type for quasi-convex mappings are proved. The constant in the classical Simpson's inequality is improved. Furthermore, the obtained bounds can be (much) better than some recently obtained bounds. Application to Simpson's quadrature rule is also given.