On Some New Dynamic Hilbert-Type Inequalities across Time Scales.

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 = q N 0 for q > 1 , which, to the best of the authors' knowledge, is a largely novel conclusion. [ABSTRACT FROM AUTHOR]