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September 5, 2025

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

Key Points

Novel characterizations of weighted hardy-type inequalities were established using nabla calculus on time scales.
Key techniques include the chain rule, minkowski's inequality, and holder's inequality to ensure results differ from classical approaches.
The examination of time scales integrates both discrete and continuous cases to enhance the understanding of inequalities.
These findings expand the application of okpoti inequality in analyzing mathematical problems within this new framework.

Abstract

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.

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