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Research Article | Open Access

Post-quantum Simpson's type inequalities for coordinated convex functions

Xue-Xiao You1, Muhammad Aamir Ali2( ), Ghulam Murtaza3, Saowaluck Chasreechai4, Sotiris K. Ntouyas5, Thanin Sitthiwirattham6( )
School of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, China
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece; Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand
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Abstract

In this paper, we prove some new Simpson's type inequalities for partial ( p , q )-differentiable convex functions of two variables in the context of ( p , q )-calculus. We also show that the findings in this paper are generalizations of comparable findings in the literature.

Keywords

Simpson's inequalities(p, q)-integralspost quantum calculusco-ordinated convexity
CLC number: 26D10, 26A51, 26D15

References

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AIMS Mathematics
Volume 7 Issue 2,
February 2022
Pages 3097-3132
DOI: 10.3934/math.2022172

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Cite this article:
You X-X, Ali MA, Murtaza G, et al. Post-quantum Simpson's type inequalities for coordinated convex functions. AIMS Mathematics, 2022, 7(2): 3097-3132. https://doi.org/10.3934/math.2022172

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Received: 23 September 2021
Accepted: 18 November 2021
Published: 15 February 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)