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On generalization of midpoint type inequalities with generalized fractional integral operators

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Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas Aims and scope Submit manuscript

Abstract

The Hermite–Hadamard inequality is the first principal result for convex functions defined on a interval of real numbers with a natural geometrical interpretation and a loose number of applications for particular inequalities. In this paper we proposed the Hermite–Hadamard and midpoint type inequalities for functions whose first and second derivatives in absolute value are s-convex through the instrument of generalized fractional integral operator and a considerable amount of results for special means which can naturally be deduced.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey

    Hüseyin Budak, Fuat Usta & Mehmet Zeki Sarikaya

  2. Department of Mathematics, Education Faculty, Uludag University, 16059, Bursa, Turkey

    M. Emin Ozdemir

Authors
  1. Hüseyin Budak
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  2. Fuat Usta
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  3. Mehmet Zeki Sarikaya
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  4. M. Emin Ozdemir
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Correspondence to Hüseyin Budak.

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Budak, H., Usta, F., Sarikaya, M.Z. et al. On generalization of midpoint type inequalities with generalized fractional integral operators. RACSAM 113, 769–790 (2019). https://doi.org/10.1007/s13398-018-0514-z

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  • DOI: https://doi.org/10.1007/s13398-018-0514-z

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