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Research Article | Open Access

Some new dynamic Steffensen-type inequalities on a general time scale measure space

Ahmed A. El-Deeb1( ), Inho Hwang2( ), Choonkil Park3, Omar Bazighifan4
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
Department of Mathematics, Incheon National University, Incheon 22012, Korea
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy
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Abstract

Our work is based on the multiple inequalities illustrated by Josip Pečarić in 2013, 1982 and Srivastava in 2017. With the help of a positive σ-finite measure, we generalize a number of those inequalities to a general time scale measure space. Besides that, in order to obtain some new inequalities as special cases, we also extend our inequalities to discrete and continuous calculus.

Keywords

Steffensen's inequalitydynamic inequalitydynamic integraltime scale
CLC number: 26D10, 26D15, 26D20, 34A12, 34A40

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AIMS Mathematics
Volume 7 Issue 3,
March 2022
Pages 4326-4337
DOI: 10.3934/math.2022240

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Cite this article:
El-Deeb AA, Hwang I, Park C, et al. Some new dynamic Steffensen-type inequalities on a general time scale measure space. AIMS Mathematics, 2022, 7(3): 4326-4337. https://doi.org/10.3934/math.2022240

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Received: 13 August 2021
Revised: 13 November 2021
Accepted: 15 November 2021
Published: 15 March 2021
©2022 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)