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The Properties of Harmonically cr - h -Convex Function and Its Applications

Author

Listed:
  • Wei Liu

    (College of Science, Hohai University, Nanjing 210098, China)

  • Fangfang Shi

    (College of Science, Hohai University, Nanjing 210098, China)

  • Guoju Ye

    (College of Science, Hohai University, Nanjing 210098, China)

  • Dafang Zhao

    (School of Mathematics and Statistics, Hubei Normal University, Huangshi 435002, China)

Abstract

In this paper, the definition of the harmonically c r - h -convex function is given, and its important properties are discussed. Jensen type inequality, Hermite–Hadamard type inequalities and Fejér type inequalities for harmonically c r - h -convex functions are also established. In addition, some numerical examples are given to verify the accuracy of the results.

Suggested Citation

  • Wei Liu & Fangfang Shi & Guoju Ye & Dafang Zhao, 2022. "The Properties of Harmonically cr - h -Convex Function and Its Applications," Mathematics, MDPI, vol. 10(12), pages 1-15, June.
    • Handle: RePEc:gam:jmathe:v:10:y:2022:i:12:p:2089-:d:840335
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    References listed on IDEAS

    as
    1. Mihai, Marcela V. & Noor, Muhammad Aslam & Noor, Khalida Inayat & Awan, Muhammad Uzair, 2015. "Some integral inequalities for harmonic h-convex functions involving hypergeometric functions," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 257-262.
    2. Chen, Feixiang, 2015. "Extensions of the Hermite–Hadamard inequality for harmonically convex functions via fractional integrals," Applied Mathematics and Computation, Elsevier, vol. 268(C), pages 121-128.
    3. Waewta Luangboon & Kamsing Nonlaopon & Jessada Tariboon & Sotiris K. Ntouyas & Hüseyin Budak, 2022. "Some ( p , q )-Integral Inequalities of Hermite–Hadamard Inequalities for ( p , q )-Differentiable Convex Functions," Mathematics, MDPI, vol. 10(5), pages 1-20, March.
    Full references (including those not matched with items on IDEAS)

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