Some new (p, q)-Dragomir–Agarwal and Iyengar type integral inequalities and their applications

Muhammad Uzair Awan; Sadia Talib; Artion Kashuri; Ibrahim Slimane; Kamsing Nonlaopon; Y. S. Hamed; Muhammad Uzair Awan; Sadia Talib; Artion Kashuri; Ibrahim Slimane; Kamsing Nonlaopon; Y. S. Hamed

doi:10.3934/math.2022317

AIMS Mathematics

2022, Volume 7, Issue 4: 5728-5751. doi: 10.3934/math.2022317

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Research article

Some new (p, q)-Dragomir–Agarwal and Iyengar type integral inequalities and their applications

1.
Department of Mathematics, Government College University, Faisalabad, Pakistan
2.
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400 Vlora, Albania
3.
Faculty of Exact Sciences and Informatics, UMAB Abdelhamid Ibn Badis University of Mostaganem, Algeria
4.
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
5.
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia

Received: 04 November 2021 Revised: 17 December 2021 Accepted: 04 January 2022 Published: 11 January 2022
MSC : 26A33, 26A51, 26D07, 26D10, 26D15, 26D20

The main objective of this paper is to derive some new post quantum analogues of Dragomir–Agarwal and Iyengar type integral inequalities essentially by using the strongly $ \varphi $-preinvexity and strongly quasi $ \varphi $-preinvexity properties of the mappings, respectively. We also discuss several new special cases which show that the results obtained are quite unifying. In order to illustrate the efficiency of our main results, some applications regarding $ ({\mathrm{p}}, {\mathrm{q}}) $-differentiable mappings that are in absolute value bounded are given.
Citation: Muhammad Uzair Awan, Sadia Talib, Artion Kashuri, Ibrahim Slimane, Kamsing Nonlaopon, Y. S. Hamed. Some new (p, q)-Dragomir–Agarwal and Iyengar type integral inequalities and their applications[J]. AIMS Mathematics, 2022, 7(4): 5728-5751. doi: 10.3934/math.2022317

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Abstract

The main objective of this paper is to derive some new post quantum analogues of Dragomir–Agarwal and Iyengar type integral inequalities essentially by using the strongly $ \varphi $-preinvexity and strongly quasi $ \varphi $-preinvexity properties of the mappings, respectively. We also discuss several new special cases which show that the results obtained are quite unifying. In order to illustrate the efficiency of our main results, some applications regarding $ ({\mathrm{p}}, {\mathrm{q}}) $-differentiable mappings that are in absolute value bounded are given.

References

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