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

  • 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.

    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

    Related Papers:

  • 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.



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