On weighted remainder form of Hardy-type inequalities

TL;DR

This paper explores a generalization of Hardy's inequality, focusing on weighted remainder forms and employing various approaches to extend previous results by Levin and Stečkin.

Contribution

It introduces new methods to analyze weighted remainder forms of Hardy-type inequalities, expanding upon Levin and Stečkin's work.

Findings

New bounds for weighted remainder Hardy inequalities

Extension of Levin and Stečkin's results to broader classes

Enhanced understanding of inequality structures

Abstract

We use different approaches to study a generalization of a result of Levin and Ste\v{c}kin concerning an inequality analogous to Hardy's inequality. Our results lead naturally to the study of weighted remainder form of Hardy-type inequalities.