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Research Article | Open Access

Unveiling new reverse Hilbert-type dynamic inequalities within the framework of Delta calculus on time scales

Haytham M. Rezk1( ), Mohammed Zakarya2, Amirah Ayidh I Al-Thaqfan3, Maha Ali3, Belal A. Glalah4( )
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt
Department of Mathematics, College of Science, King Khalid University, P.O. Box 9004, Abha 61413, Saudi Arabia
Department of Mathematics, College of Arts and Sciences, King Khalid University, P.O. Box 64512, Abha 62529, Sarat Ubaidah, Saudi Arabia
Department of Basic Science, Higher Technological Institute, Sixth of October, October 12573, Egypt
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Abstract

Some new reverse versions of Hilbert-type inequalities are studied in this paper. The results are established by applying the time scale versions of reverse Hölder's inequality, reverse Jensen's inequality, chain rule on time scales, and the mean inequality. As applications, some particular results (when T = N and T = R ) are considered. Our results provide some new estimates for these types of inequalities and improve some of those recently published in the literature.

Keywords

Hilbert-type inequalitiesreverse Hilbert-type inequalitydelta calculustime scales
CLC number: 26D10, 26D15, 42B25, 42C10, 47B38

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AIMS Mathematics
Volume 10 Issue 2,
February 2025
Pages 2254-2276
DOI: 10.3934/math.2025104

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Rezk HM, Zakarya M, Al-Thaqfan AAI, et al. Unveiling new reverse Hilbert-type dynamic inequalities within the framework of Delta calculus on time scales. AIMS Mathematics, 2025, 10(2): 2254-2276. https://doi.org/10.3934/math.2025104

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Received: 31 August 2024
Revised: 05 January 2025
Accepted: 10 January 2025
Published: 15 February 2025
©2025 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0)