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Inequalities for fractional integral with the use of stochastic orderings

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  • Epebinu, Abayomi Dennis
  • Szostok, Tomasz

Abstract

In this paper, we show the connections of inequalities involving fractional integrals with Ohlin lemma and Levin-Stechkin theorem. First, we give a new proof of the fractional version of the inequality of Hermite Hadamard type and then we extend it in two directions. Thus we compare the fractional expression occurring in this inequality with the usual integral and we obtain stronger inequalities (one of them is related to Bullen inequality).

Suggested Citation

  • Epebinu, Abayomi Dennis & Szostok, Tomasz, 2024. "Inequalities for fractional integral with the use of stochastic orderings," Applied Mathematics and Computation, Elsevier, vol. 466(C).
    • Handle: RePEc:eee:apmaco:v:466:y:2024:i:c:s0096300323006501
    DOI: 10.1016/j.amc.2023.128481
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    References listed on IDEAS

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    1. Ohlin, Jan, 1969. "On a class of measures of dispersion with application to optimal reinsurance," ASTIN Bulletin, Cambridge University Press, vol. 5(2), pages 249-266, May.
    2. Set, Erhan & İşcan, İmdat & Zeki Sarikaya, M. & Emin Özdemir, M., 2015. "On new inequalities of Hermite–Hadamard–Fejér type for convex functions via fractional integrals," Applied Mathematics and Computation, Elsevier, vol. 259(C), pages 875-881.
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