On Some New Dynamic Hilbert-Type Inequalities across Time Scales-Reference-Cited by-同舟云学术

On Some New Dynamic Hilbert-Type Inequalities across Time Scales

Published:2024-07-14 Issue:7 Volume:13 Page:475
ISSN:2075-1680
Container-title:Axioms
language:en
Short-container-title:Axioms

Author:

Zakarya Mohammed¹^ORCID,Saied Ahmed I.²³,Al-Thaqfan Amirah Ayidh I⁴,Ali Maha⁴,Rezk Haytham M.⁵^ORCID

Affiliation:

1. Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia

2. Mathematical Institute, Slovak Academy of Sciences, Grekošákova 6, 04001 Košice, Slovakia

3. Department of Mathematics, Faculty of Science, Benha University, Benha 13511, Egypt

4. Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Sarat Ubaidah, Saudi Arabia

5. Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt

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.

Funder

Deanship of Research and Graduate Studies at King Khalid University

Publisher

MDPI AG

Link

https://www.mdpi.com/2075-1680/13/7/475/pdf

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