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A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results

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  • Shin Min Kang

    (Department of Mathematics and Research Institute of Natural Science, Gyeongsang National University, Jinju 52828, Korea
    Center for General Education, China Medical University, Taichung 40402, Taiwan)

  • Ghulam Abbas

    (Department of Mathematics, Government College Bhalwal, Sargodha 40100, Pakistan
    Department of Mathematics, University of Sargodha, Sargodha 40100, Pakistan)

  • Ghulam Farid

    (Department of Mathematics, COMSATS University Islamabad, Attock Campus 43600, Pakistan)

  • Waqas Nazeer

    (Division of Science and Technology, University of Education, Lahore 54000, Pakistan)

Abstract

In this paper, we obtain a version of the Fejér–Hadamard inequality for harmonically convex functions via generalized fractional integral operator. In addition, we establish an integral identity and some Fejér–Hadamard type integral inequalities for harmonically convex functions via a generalized fractional integral operator. Being generalizations, our results reproduce some known results.

Suggested Citation

  • Shin Min Kang & Ghulam Abbas & Ghulam Farid & Waqas Nazeer, 2018. "A Generalized Fejér–Hadamard Inequality for Harmonically Convex Functions via Generalized Fractional Integral Operator and Related Results," Mathematics, MDPI, vol. 6(7), pages 1-16, July.
    • Handle: RePEc:gam:jmathe:v:6:y:2018:i:7:p:122-:d:157483
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    References listed on IDEAS

    as
    1. İmdat İşcan, 2014. "On Some New Hermite-Hadamard Type Inequalities for s -Geometrically Convex Functions," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2014, pages 1-8, June.
    2. Feixiang Chen & Shanhe Wu, 2014. "Fejér and Hermite-Hadamard Type Inequalities for Harmonically Convex Functions," Journal of Applied Mathematics, Hindawi, vol. 2014, pages 1-6, August.
    3. İmdat İşcan, 2014. "Hermite-Hadamard and Simpson-Like Type Inequalities for Differentiable Harmonically Convex Functions," Journal of Mathematics, Hindawi, vol. 2014, pages 1-10, June.
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