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Research Article | Open Access

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

Elkhateeb S. Aly1,2A. I. Saied3I. Ibedou3Mohamed S. Algolam4Wael 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

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 T corresponds to the real numbers (when T = R ). Additionally, we derive distinct inequalities within the realm of time scale calculus, such as cases T = N and q N for q > 1. These findings represent new and significant contributions for the reader.

CLC number: 26D10, 26D15, 34N05, 47B38, 39A12

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AIMS Mathematics
Pages 11156-11179

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Cite this article:
Aly ES, Saied AI, Ibedou I, et al. Some new generalizations of reversed Minkowski's inequality for several functions via time scales. AIMS Mathematics, 2024, 9(5): 11156-11179. https://doi.org/10.3934/math.2024547

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Received: 16 February 2024
Revised: 11 March 2024
Accepted: 18 March 2024
Published: 15 May 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)