Fractional Ostrowski type inequalities for differentiable harmonically convex functions

Thanin Sitthiwirattham; Muhammad Aamir Ali; Hüseyin Budak; Sotiris K. Ntouyas; Chanon Promsakon; Thanin Sitthiwirattham; Muhammad Aamir Ali; Hüseyin Budak; Sotiris K. Ntouyas; Chanon Promsakon

doi:10.3934/math.2022217

AIMS Mathematics

2022, Volume 7, Issue 3: 3939-3958. doi: 10.3934/math.2022217

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Research article

Fractional Ostrowski type inequalities for differentiable harmonically convex functions

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, Dü zce University, Düzce-Turkey
4.
Department of Mathematics, University of Ioannina, 451 10 Ioannina, Greece
5.
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.
Department of Mathematics, Faculty of Applied Science, King Mongkut's University of Technology North Bangkok, Bangkok, 10800, Thailand

Received: 01 August 2021 Accepted: 28 November 2021 Published: 10 December 2021
MSC : 26D07, 26D10, 26D15

In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.
- Hermite-Hadamard inequalities,
- generalized fractional integrals,
- harmonically convex functions
Citation: Thanin Sitthiwirattham, Muhammad Aamir Ali, Hüseyin Budak, Sotiris K. Ntouyas, Chanon Promsakon. Fractional Ostrowski type inequalities for differentiable harmonically convex functions[J]. AIMS Mathematics, 2022, 7(3): 3939-3958. doi: 10.3934/math.2022217

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Abstract

In this paper, we prove some new Ostrowski type inequalities for differentiable harmonically convex functions using generalized fractional integrals. Since we are using generalized fractional integrals to establish these inequalities, therefore we obtain some new inequalities of Ostrowski type for Riemann-Liouville fractional integrals and $ k $-Riemann-Liouville fractional integrals in special cases. Finally, we give some applications to special means of real numbers for newly established inequalities.

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