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 Hölder'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.