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Research Article | Open Access

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

Muhammad Uzair Awan1, Sadia Talib1, Artion Kashuri2, Ibrahim Slimane3, Kamsing Nonlaopon4( ), Y. S. Hamed5
Department of Mathematics, Government College University, Faisalabad, Pakistan
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400 Vlora, Albania
Faculty of Exact Sciences and Informatics, UMAB Abdelhamid Ibn Badis University of Mostaganem, Algeria
Department of Mathematics, Faculty of Science, Khon Kaen University, Khon Kaen 40002, Thailand
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
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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 φ-preinvexity and strongly quasi φ-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 ( p , q )-differentiable mappings that are in absolute value bounded are given.

Keywords

Dragomir–Agarwal type inequalityIyengar type inequality(p, q)-integralstrongly φ-preinvex mappingpost quantum calculusbounded functions
CLC number: 26A33, 26A51, 26D07, 26D10, 26D15, 26D20

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AIMS Mathematics
Volume 7 Issue 4,
April 2022
Pages 5728-5751
DOI: 10.3934/math.2022317

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Cite this article:
Awan MU, Talib S, Kashuri A, et al. Some new (p, q)-Dragomir–Agarwal and Iyengar type integral inequalities and their applications. AIMS Mathematics, 2022, 7(4): 5728-5751. https://doi.org/10.3934/math.2022317

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Received: 04 November 2021
Revised: 17 December 2021
Accepted: 04 January 2022
Published: 15 April 2022
©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)