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Research Article | Open Access

N-dimension for dynamic generalized inequalities of Hölder and Minkowski type on diamond alpha time scales

Elkhateeb S. Aly1,2( ), Ali M. Mahnashi1, Abdullah A. Zaagan1, I. Ibedou3, A. I. Saied3, Wael W. Mohammed4,5
Department of Mathematics, College of Science, Jazan University, P. O. Box 114, Jazan 45142, Kingdom of Saudi Arabia
Nanotechnology Research Unit, College of Science, Jazan University, P. O. Box 114, Jazan 45142, Saudi Arabia
Department of Mathematics, Faculty of Science, Benha university, Benha, Egypt
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt
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Abstract

Expanding on our research, this paper introduced novel generalizations of H ölder's and Minkowski's dynamic inequalities on diamond alpha time scales. Specifically, as particular instances of our findings, we replicated the discrete inequalities established when T = N . Furthermore, our investigation extended to the continuous case with T = R , revealing additional inequalities that are both new and valuable for readers seeking a comprehensive understanding of the topic.

Keywords

Hölder's inequalityinequalities on time scalesMinkowski's inequalitydiamond alpha calculus
CLC number: 26D10, 26D15, 34N05, 39A12, 47B38

References

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AIMS Mathematics
Volume 9 Issue 4,
April 2024
Pages 9329-9347
DOI: 10.3934/math.2024454

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Cite this article:
Aly ES, Mahnashi AM, Zaagan AA, et al. N-dimension for dynamic generalized inequalities of Hölder and Minkowski type on diamond alpha time scales. AIMS Mathematics, 2024, 9(4): 9329-9347. https://doi.org/10.3934/math.2024454

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Received: 20 January 2023
Revised: 19 February 2024
Accepted: 01 March 2024
Published: 15 April 2024
©2024 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)