Some new generalizations of reversed Minkowski's inequality for several functions via time scales

Elkhateeb S. Aly; A. I. Saied; I. Ibedou; Mohamed S. Algolam; Wael W. Mohammed; Elkhateeb S. Aly; A. I. Saied; I. Ibedou; Mohamed S. Algolam; Wael W. Mohammed

doi:10.3934/math.2024547

AIMS Mathematics

2024, Volume 9, Issue 5: 11156-11179. doi: 10.3934/math.2024547

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Some new generalizations of reversed Minkowski's inequality for several functions via 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: 16 February 2024 Revised: 11 March 2024 Accepted: 18 March 2024 Published: 21 March 2024
MSC : 26D10, 26D15, 34N05, 47B38, 39A12

In this paper, we introduce novel extensions of the reversed Minkowski inequality for various functions defined on time scales. Our approach involves the application of Jensen's and Hölder's inequalities on time scales. Our results encompass the continuous inequalities established by Benaissa as special cases when the time scale $ \mathbb{T} $ corresponds to the real numbers (when $ \mathbb{T = R} $). Additionally, we derive distinct inequalities within the realm of time scale calculus, such as cases $ \mathbb{ T = N} $ and $ q^{\mathbb{N}} $ for $ q > 1 $. These findings represent new and significant contributions for the reader.
- Hölder's inequality,
- inequalities on time scales,
- Jensen's inequality
Citation: Elkhateeb S. Aly, A. I. Saied, I. Ibedou, Mohamed S. Algolam, Wael W. Mohammed. Some new generalizations of reversed Minkowski's inequality for several functions via time scales[J]. AIMS Mathematics, 2024, 9(5): 11156-11179. doi: 10.3934/math.2024547

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Abstract

In this paper, we introduce novel extensions of the reversed Minkowski inequality for various functions defined on time scales. Our approach involves the application of Jensen's and Hölder's inequalities on time scales. Our results encompass the continuous inequalities established by Benaissa as special cases when the time scale $ \mathbb{T} $ corresponds to the real numbers (when $ \mathbb{T = R} $). Additionally, we derive distinct inequalities within the realm of time scale calculus, such as cases $ \mathbb{ T = N} $ and $ q^{\mathbb{N}} $ for $ q > 1 $. These findings represent new and significant contributions for the reader.

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