Some companions of perturbed Ostrowski type inequalities for functions whose second derivatives are bounded and application

TL;DR

This paper develops new inequalities related to Ostrowski type integrals for functions with bounded second derivatives, and demonstrates their applications in numerical integration and probability density functions.

Contribution

It introduces novel companions of perturbed Ostrowski inequalities specifically for functions with bounded second derivatives, expanding their theoretical and practical scope.

Findings

Derived new inequalities for functions with bounded second derivatives.

Applied inequalities to improve composite quadrature rules.

Extended applications to probability density functions.

Abstract

In this paper we establish some companions of perturbed Ostrowski type integral inequalities for functions whose second derivatives are bounded. Some applications to composite quadrature rules, and to probability density functions are also given.