New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel

Hari M. Srivastava; Artion Kashuri; Pshtiwan Othman Mohammed; Abdullah M. Alsharif; Juan L. G. Guirao; Hari M. Srivastava; Artion Kashuri; Pshtiwan Othman Mohammed; Abdullah M. Alsharif; Juan L. G. Guirao

doi:10.3934/math.2021648

AIMS Mathematics

2021, Volume 6, Issue 10: 11167-11186. doi: 10.3934/math.2021648

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New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel

1.
Department of Mathematics and Statistics, University of Victoria, Victoria, British Columbia V8W 3R4, Canada
2.
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan
3.
Department of Mathematics and Informatics, Azerbaijan University, 71 Jeyhun Hajibeyli Street, AZ1007 Baku, Azerbaijan
4.
Section of Mathematics, International Telematic University Uninettuno, I-$ 00186 $ Rome, Italy
5.
Department of Mathematics, Faculty of Technical Science, University "Ismail Qemali", 9400 Vlora, Albania
6.
Department of Mathematics, College of Education, University of Sulaimani, Sulaimani, Kurdistan Region, Iraq
7.
Department of Mathematics and Statistics, College of Science, Taif University, P. O. Box 11099, Taif 21944, Saudi Arabia
8.
Departamento de Matemática Aplicada y Estadística, Universidad Politécnica de Cartagena, Campus de la Muralla, 30203 Cartagena, Murcia, Spain
9.
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

Received: 13 May 2021 Accepted: 08 July 2021 Published: 03 August 2021
MSC : 26D15, 26D10, 26A33

The main goal of this article is first to introduce a new generalization of the fractional integral operators with a certain modified Mittag-Leffler kernel and then investigate the Chebyshev inequality via this general family of fractional integral operators. We improve our results and we investigate the Chebyshev inequality for more than two functions. We also derive some inequalities of this type for functions whose derivatives are bounded above and bounded below. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. Finally, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view.
- Chebyshev inequality,
- generalized fractional integrals,
- modified Mittag-Leffler kernel,
- Fox-Wright function,
- integral inequalities
Citation: Hari M. Srivastava, Artion Kashuri, Pshtiwan Othman Mohammed, Abdullah M. Alsharif, Juan L. G. Guirao. New Chebyshev type inequalities via a general family of fractional integral operators with a modified Mittag-Leffler kernel[J]. AIMS Mathematics, 2021, 6(10): 11167-11186. doi: 10.3934/math.2021648

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Abstract

The main goal of this article is first to introduce a new generalization of the fractional integral operators with a certain modified Mittag-Leffler kernel and then investigate the Chebyshev inequality via this general family of fractional integral operators. We improve our results and we investigate the Chebyshev inequality for more than two functions. We also derive some inequalities of this type for functions whose derivatives are bounded above and bounded below. In addition, we establish an estimate for the Chebyshev functional by using the new fractional integral operators. Finally, we find similar inequalities for some specialized fractional integrals keeping some of the earlier results in view.

References

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