On Innovative Conditions for Weighted Hardy-Type Inequalities on Time Scales

Abstract

This article presents necessary and sufficient conditions for novel characterizations of weighted Hardy-type inequalities applying the chain rule, Minkowski's inequality, and H & ouml;lder's inequality with nabla calculus on time scales. Properties of time scales and Okpoti inequality are exploited to derive our results. These results differ from classical weighted Hardy-type inequalities because they are examined on time scales that combine discrete and continuous cases.