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Some Generalized Hadamard–Type Inequalities via Fractional Integrals

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Abstract

In this paper, we establish some generalized inequalities of the Hermite–Hadamard type using fractional Riemann–Liouville integrals for the class of s-convex functions in the first and second sense. We assume that second derivatives of these functions are convex and take on values at intermediate points of the interval under consideration. We prove that this approach reduces the absolute error of Hadamard-type inequalities by a multiple of the number of intermediate points. In a particular case, the obtained upper bounds for the Hadamard inequality coincide with those given in the literature.

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Authors and Affiliations

  1. Bursa Uludag University, 16059, Bursa, Turkey

    B. Bayraktar

  2. Institute of Applied Mathematics and Automation of Kabardino–Balkar Scientific Centre of RAS, 89a A. Shortanova str., 360000, Nalchik, Russia

    A. Kh. Attaev

  3. Institute of Computer Science and Problems of Regional Management of Kabardino–Balkar Scientific Centre of RAS, 37A I. Armand str., 360000, Nalchik, Russia

    V. Ch. Kudaev

Authors
  1. B. Bayraktar
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  2. A. Kh. Attaev
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  3. V. Ch. Kudaev
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Correspondence to B. Bayraktar, A. Kh. Attaev or V. Ch. Kudaev.

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Russian Text © The Author(s), 2021, published in Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2021, No. 2, pp. 3–18.

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Bayraktar, B., Attaev, A.K. & Kudaev, V.C. Some Generalized Hadamard–Type Inequalities via Fractional Integrals. Russ Math. 65, 1–14 (2021). https://doi.org/10.3103/S1066369X21020018

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  • DOI: https://doi.org/10.3103/S1066369X21020018

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