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

Xue-Xiao You; Muhammad Aamir Ali; Ghulam Murtaza; Saowaluck Chasreechai; Sotiris K. Ntouyas; Thanin Sitthiwirattham; Xue-Xiao You; Muhammad Aamir Ali; Ghulam Murtaza; Saowaluck Chasreechai; Sotiris K. Ntouyas; Thanin Sitthiwirattham

doi:10.3934/math.2022172

AIMS Mathematics

2022, Volume 7, Issue 2: 3097-3132. doi: 10.3934/math.2022172

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Research article

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

1.
School of Mathematics and Statistics, Hubei Normal University, Huangshi, Hubei 435002, China
2.
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China
3.
Department of Mathematics, University of Management and Technology, Lahore, Pakistan
4.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand
5.
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
6.
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand

Received: 23 September 2021 Accepted: 18 November 2021 Published: 24 November 2021
MSC : 26D10, 26A51, 26D15

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.
- Simpson's inequalities,
- $ \left(p, q\right) $-integrals,
- post quantum calculus,
- co-ordinated convexity
Citation: Xue-Xiao You, Muhammad Aamir Ali, Ghulam Murtaza, Saowaluck Chasreechai, Sotiris K. Ntouyas, Thanin Sitthiwirattham. Post-quantum Simpson's type inequalities for coordinated convex functions[J]. AIMS Mathematics, 2022, 7(2): 3097-3132. doi: 10.3934/math.2022172

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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.

References

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