Quantum Hermite-Hadamard type integral inequalities for convex stochastic processes

Thanin Sitthiwirattham; Muhammad Aamir Ali; Hüseyin Budak; Saowaluck Chasreechai; Thanin Sitthiwirattham; Muhammad Aamir Ali; Hüseyin Budak; Saowaluck Chasreechai

doi:10.3934/math.2021695

AIMS Mathematics

2021, Volume 6, Issue 11: 11989-12010. doi: 10.3934/math.2021695

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Research article

Quantum Hermite-Hadamard type integral inequalities for convex stochastic processes

1.
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok, 10300, Thailand
2.
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing, 210023, China
3.
Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey
4.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand

Received: 19 July 2021 Accepted: 15 August 2021 Published: 17 August 2021
MSC : 26D10, 26D15, 26A51

In this paper, we introduce the notions of $ q $-mean square integral for stochastic processes and co-ordinated stochastic processes. Furthermore, we establish some new quantum Hermite-Hadamard type inequalities for convex stochastic processes and co-ordinated stochastic processes via newly defined integrals. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as $ q, \; q_{1}, \; q_{2}\rightarrow 1^{-} $ in the newly obtained results.
- Hermite-Hadamard inequality,
- Jensen inequality,
- convex stochastic processes
Citation: Thanin Sitthiwirattham, Muhammad Aamir Ali, Hüseyin Budak, Saowaluck Chasreechai. Quantum Hermite-Hadamard type integral inequalities for convex stochastic processes[J]. AIMS Mathematics, 2021, 6(11): 11989-12010. doi: 10.3934/math.2021695

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Abstract

In this paper, we introduce the notions of $ q $-mean square integral for stochastic processes and co-ordinated stochastic processes. Furthermore, we establish some new quantum Hermite-Hadamard type inequalities for convex stochastic processes and co-ordinated stochastic processes via newly defined integrals. It is also revealed that the results presented in this research transformed into some already proved results by considering the limits as $ q, \; q_{1}, \; q_{2}\rightarrow 1^{-} $ in the newly obtained results.

References

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