One-dimensional integral Rellich type inequalities

TL;DR

This paper develops new sharp integral Hardy-Rellich and Rellich inequalities, improving previous results and introducing novel inequalities in the mathematical analysis of integral inequalities.

Contribution

It presents the first sharp integral Rellich inequality and improves existing Hardy-Rellich inequalities in the context of integral forms.

Findings

Sharp Hardy-Rellich inequality established

New sharp Rellich integral inequality derived

Improvement over previous inequalities achieved

Abstract

The motive of this note is twofold. Inspired by the recent development of a new kind of Hardy inequality, here we discuss the corresponding Hardy-Rellich and Rellich inequality versions in the integral form. The obtained sharp Hardy-Rellich type inequality improves the previously known result. Meanwhile, the established sharp Rellich type integral inequality seems new.