论跨时间尺度的一些新动态希尔伯特式不等式

Axioms Pub Date : 2024-07-14 DOI:10.3390/axioms13070475

M. Zakarya, A. Saied, Amirah Ayidh I Al-Thaqfan, M. Ali, H. M. Rezk

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摘要

在本文中，我们利用荷尔德不等式、链式法则和均值不等式，在时间尺度 T 的框架内提出了一些新颖的动态希尔伯特式不等式。作为我们研究成果的具体实例（当 T=N 和 T=R 时），我们得到了以前建立的不等式的离散和连续类比。此外，我们还推导出了不同时间尺度的其他不等式，例如 q>1 时的 T=qN0，据作者所知，这在很大程度上是一个新结论。

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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=qN0 for q>1, which, to the best of the authors’ knowledge, is a largely novel conclusion.

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