Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for $ s $-convex functions in the second sense with applications

Suphawat Asawasamrit; Muhammad Aamir Ali; Hüseyin Budak; Sotiris K. Ntouyas; Jessada Tariboon; Suphawat Asawasamrit; Muhammad Aamir Ali; Hüseyin Budak; Sotiris K. Ntouyas; Jessada Tariboon

doi:10.3934/math.2021771

AIMS Mathematics

2021, Volume 6, Issue 12: 13327-13346. doi: 10.3934/math.2021771

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Research article

Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for $ s $-convex functions in the second sense with applications

1.
Intelligent and Nonlinear Dynamic Innovations Research Center, Department of Mathematics, Faculty of Applied Sciences, King Mongkut's University of Technology North Bangkok, Bangkok 10800, Thailand
2.
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
3.
Department of Mathematics, Faculty of Arts and Sciences, Düzce University, Düzce, Turkey
4.
Department of Mathematics, University of Ioannina, 45110 Ioannina, Greece
5.
Nonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Sciences, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia

Received: 12 July 2021 Accepted: 10 September 2021 Published: 16 September 2021
MSC : 26D10, 26A51, 26D15

In this study, we use quantum calculus to prove Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in the second sense. The newly proven results are also shown to be an extension of comparable results in the existing literature. Furthermore, it is provided that how the newly discovered inequalities can be applied to special means of real numbers.
- Hermite-Hadamard inequality,
- Ostrowski inequality,
- $ q $ -integral,
- quantum calculus,
- $ s $-convex functions
Citation: Suphawat Asawasamrit, Muhammad Aamir Ali, Hüseyin Budak, Sotiris K. Ntouyas, Jessada Tariboon. Quantum Hermite-Hadamard and quantum Ostrowski type inequalities for $ s $-convex functions in the second sense with applications[J]. AIMS Mathematics, 2021, 6(12): 13327-13346. doi: 10.3934/math.2021771

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Abstract

In this study, we use quantum calculus to prove Hermite-Hadamard and Ostrowski type inequalities for s-convex functions in the second sense. The newly proven results are also shown to be an extension of comparable results in the existing literature. Furthermore, it is provided that how the newly discovered inequalities can be applied to special means of real numbers.

References

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