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Volume 13
Issue 9
10.3390/sym13091724
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Article

On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables

by
Thanin Sitthiwirattham
1,*,
Hüseyin Budak
2,
Hasan Kara
2,
Muhammad Aamir Ali
3,* and
Jiraporn Reunsumrit
4
1
Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand
2
Department of Mathematics, Faculty of Science and Arts, Düzce University, 81620 Düzce, Turkey
3
Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China
4
Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand
*
Authors to whom correspondence should be addressed.
Symmetry 2021, 13(9), 1724; https://doi.org/10.3390/sym13091724
Submission received: 31 August 2021 / Revised: 15 September 2021 / Accepted: 16 September 2021 / Published: 17 September 2021
(This article belongs to the Special Issue Symmetry in the Mathematical Inequalities)
Versions Notes

Abstract

In this paper, we first prove three identities for functions of bounded variations. Then, by using these equalities, we obtain several trapezoid- and Ostrowski-type inequalities via generalized fractional integrals for functions of bounded variations with two variables. Moreover, we present some results for Riemann–Liouville fractional integrals by special choice of the main results. Finally, we investigate the connections between our results and those in earlier works. Analytic inequalities of this nature and especially the techniques involved have applications in various areas in which symmetry plays a prominent role.
Keywords: trapezoid-type inequality; fractional integrals; functions of bounded variations trapezoid-type inequality; fractional integrals; functions of bounded variations

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MDPI and ACS Style

Sitthiwirattham, T.; Budak, H.; Kara, H.; Ali, M.A.; Reunsumrit, J. On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables. Symmetry 2021, 13, 1724. https://doi.org/10.3390/sym13091724

AMA Style

Sitthiwirattham T, Budak H, Kara H, Ali MA, Reunsumrit J. On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables. Symmetry. 2021; 13(9):1724. https://doi.org/10.3390/sym13091724

Chicago/Turabian Style

Sitthiwirattham, Thanin, Hüseyin Budak, Hasan Kara, Muhammad Aamir Ali, and Jiraporn Reunsumrit. 2021. "On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables" Symmetry 13, no. 9: 1724. https://doi.org/10.3390/sym13091724

APA Style

Sitthiwirattham, T., Budak, H., Kara, H., Ali, M. A., & Reunsumrit, J. (2021). On Some New Fractional Ostrowski- and Trapezoid-Type Inequalities for Functions of Bounded Variations with Two Variables. Symmetry, 13(9), 1724. https://doi.org/10.3390/sym13091724

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