On Some New Dynamic Hilbert-Type Inequalities across Time Scales

Abstract

In this article, we present some novel dynamic Hilbert-type inequalities within the framework of time scales T. We achieve this by utilizing Hölder’s inequality, the chain rule, and the mean inequality. As specific instances of our findings (when T=N and T=R), we obtain the discrete and continuous analogues of previously established inequalities. Additionally, we derive other inequalities for different time scales, such as T=qN0 for q>1, which, to the best of the authors’ knowledge, is a largely novel conclusion.

Keywords

• Hilbert-type inequalities
• Hölder’s inequality
• chain rule
• mean inequality
• dynamic inequality
• time scale delta calculus