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Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s -Convexity on Fractal Sets

Author

Listed:
  • Ohud Almutairi

    (Department of Mathematics, University of Hafr Al-Batin, Hafr Al-Batin 31991, Saudi Arabia
    These authors contributed equally to this work.)

  • Adem Kılıçman

    (Department of Mathematics and Institute for Mathematical Research, University Putra Malaysia, Serdang 43400, Malaysia
    These authors contributed equally to this work.)

Abstract

In this article, we establish new Hermite–Hadamard-type inequalities via Riemann–Liouville integrals of a function ψ taking its value in a fractal subset of R and possessing an appropriate generalized s -convexity property. It is shown that these fractal inequalities give rise to a generalized s -convexity property of ψ . We also prove certain inequalities involving Riemann–Liouville integrals of a function ψ provided that the absolute value of the first or second order derivative of ψ possesses an appropriate fractal s -convexity property.

Suggested Citation

  • Ohud Almutairi & Adem Kılıçman, 2019. "Generalized Integral Inequalities for Hermite–Hadamard-Type Inequalities via s -Convexity on Fractal Sets," Mathematics, MDPI, vol. 7(11), pages 1-16, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1065-:d:284221
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    References listed on IDEAS

    as
    1. Huixia Mo & Xin Sui, 2014. "Generalized -Convex Functions on Fractal Sets," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-8, July.
    2. X. M. Yang, 2001. "On E-Convex Sets, E-Convex Functions, and E-Convex Programming," Journal of Optimization Theory and Applications, Springer, vol. 109(3), pages 699-704, June.
    3. Huixia Mo & Xin Sui & Dongyan Yu, 2014. "Generalized Convex Functions on Fractal Sets and Two Related Inequalities," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-7, June.
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