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

Ahmed A. El-Deeb; Inho Hwang; Choonkil Park; Omar Bazighifan; Ahmed A. El-Deeb; Inho Hwang; Choonkil Park; Omar Bazighifan

doi:10.3934/math.2022240

AIMS Mathematics

2022, Volume 7, Issue 3: 4326-4337. doi: 10.3934/math.2022240

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Research article

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

1.
Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt
2.
Department of Mathematics, Incheon National University, Incheon 22012, Korea
3.
Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea
4.
Section of Mathematics, International Telematic University Uninettuno, Corso Vittorio Emanuele II, 39, 00186 Rome, Italy

Received: 13 August 2021 Revised: 13 November 2021 Accepted: 15 November 2021 Published: 20 December 2021
MSC : 26D10, 26D15, 26D20, 34A12, 34A40

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 $ \sigma $-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.
- Steffensen's inequality,
- dynamic inequality,
- dynamic integral,
- time scale
Citation: Ahmed A. El-Deeb, Inho Hwang, Choonkil Park, Omar Bazighifan. Some new dynamic Steffensen-type inequalities on a general time scale measure space[J]. AIMS Mathematics, 2022, 7(3): 4326-4337. doi: 10.3934/math.2022240

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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 $ \sigma $-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.

References

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