A companion of Ostrowski like inequality for mappings whose second derivatives belong to $L^{\infty}$ spaces and applications

TL;DR

This paper establishes a new Ostrowski-like inequality for functions with bounded second derivatives and demonstrates its applications in numerical integration and probability density functions.

Contribution

It introduces a novel inequality for functions with second derivatives in $L^{ abla}$ spaces, extending Ostrowski's inequality and applying it to quadrature rules and probability densities.

Findings

Derived a new Ostrowski-like inequality for $L^{ abla}$ second derivatives.

Applied the inequality to improve composite quadrature rules.

Extended the inequality's use to probability density functions.

Abstract

A companion of Ostrowski like inequality for mappings whose second derivatives belong to $L^{\infty}$ spaces is established. Applications to composite quadrature rules, and to probability density functions are also given.