Some New Hardy-Type Inequalities with Negative Parameters on Time Scales

Abstract In this paper, we present new Hardy-type inequalities with negative parameters on a time scale $${\mathbb {T}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>T</mml:mi> </mml:math> . The adopted approach draws upon the use of a reversed Hölder dynamic inequality, a chain rule, and the integration by parts rule on time scales. In the continuous case, our results contain integral inequalities due to Benaissa and Budak, while in the discrete case, the obtained inequalities are essentially new. Additionally, we demonstrate the applicability of our results in the quantum case.