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

Elkhateeb S. Aly; Ali M. Mahnashi; Abdullah A. Zaagan; I. Ibedou; A. I. Saied; Wael W. Mohammed; Elkhateeb S. Aly; Ali M. Mahnashi; Abdullah A. Zaagan; I. Ibedou; A. I. Saied; Wael W. Mohammed

doi:10.3934/math.2024454

AIMS Mathematics

2024, Volume 9, Issue 4: 9329-9347. doi: 10.3934/math.2024454

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

1.
Department of Mathematics, College of Science, Jazan University, P. O. Box 114, Jazan 45142, Kingdom of Saudi Arabia
2.
Nanotechnology Research Unit, College of Science, Jazan University, P. O. Box 114, Jazan 45142, Saudi Arabia
3.
Department of Mathematics, Faculty of Science, Benha university, Benha, Egypt
4.
Department of Mathematics, College of Science, University of Ha'il, Ha'il 2440, Saudi Arabia
5.
Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, Egypt

Received: 20 January 2023 Revised: 19 February 2024 Accepted: 01 March 2024 Published: 06 March 2024
MSC : 26D10, 26D15, 34N05, 39A12, 47B38

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 $ \mathbb{T = N} $. Furthermore, our investigation extended to the continuous case with $ \mathbb{ T = R} $, revealing additional inequalities that are both new and valuable for readers seeking a comprehensive understanding of the topic.
- Hölder's inequality,
- inequalities on time scales,
- Minkowski's inequality,
- diamond alpha calculus
Citation: Elkhateeb S. Aly, Ali M. Mahnashi, Abdullah A. Zaagan, I. Ibedou, A. I. Saied, Wael W. Mohammed. N-dimension for dynamic generalized inequalities of Hölder and Minkowski type on diamond alpha time scales[J]. AIMS Mathematics, 2024, 9(4): 9329-9347. doi: 10.3934/math.2024454

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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 $ \mathbb{T = N} $. Furthermore, our investigation extended to the continuous case with $ \mathbb{ T = R} $, revealing additional inequalities that are both new and valuable for readers seeking a comprehensive understanding of the topic.

References

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