Some dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus

Abstract

In this paper, we establish some new dynamic Hardy-type inequalities with negative parameters on time scales nabla calculus by applying the reverse H ölder's inequality, integration by parts, and chain rule on time scales nabla calculus. As special cases of our results (when $ \mathbb{ T = R} $), we get the continuous analouges of inequalities proven by Benaissa and Sarikaya, and when $ \mathbb{T = N}_{0} $, the results to the best of the authors' knowledge are essentially new.

Keywords

• hardy-type inequalities with negative parameters
• time scales
• reverse hölder's inequality
• chain rule