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Some Remarks on Local Fractional Integral Inequalities Involving Mittag–Leffler Kernel Using Generalized ( E , h )-Convexity

Author

Listed:
  • Wedad Saleh

    (Department of Mathematics, Taibah University, Al-Medina 42353, Saudi Arabia)

  • Abdelghani Lakhdari

    (Department CPST, Ecole Nationale Supérieure de Technologie et d’Ingénierie, Annaba 23005, Algeria)

  • Ohud Almutairi

    (Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia)

  • Adem Kiliçman

    (Department of Mathematics and Statistics, Universiti Putra Malaysia (UPM), Serdang 43400, Malaysia)

Abstract

In the present work, we introduce two new local fractional integral operators involving Mittag–Leffler kernel on Yang’s fractal sets. Then, we study the related generalized Hermite–Hadamard-type inequality using generalized ( E , h ) -convexity and obtain two identities pertaining to these operators, and the respective first- and second-order derivatives are given. In terms of applications, we provide some new generalized trapezoid-type inequalities for generalized ( E , h )-convex functions. Finally, some special cases are deduced for different values of δ , E , and h .

Suggested Citation

  • Wedad Saleh & Abdelghani Lakhdari & Ohud Almutairi & Adem Kiliçman, 2023. "Some Remarks on Local Fractional Integral Inequalities Involving Mittag–Leffler Kernel Using Generalized ( E , h )-Convexity," Mathematics, MDPI, vol. 11(6), pages 1-13, March.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:6:p:1373-:d:1094843
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    References listed on IDEAS

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    1. Sarikaya, Mehmet Zeki & Tunc, Tuba & Budak, Hüseyin, 2016. "On generalized some integral inequalities for local fractional integrals," Applied Mathematics and Computation, Elsevier, vol. 276(C), pages 316-323.
    2. E. A. Youness, 1999. "E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 102(2), pages 439-450, August.
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