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Extensions of the Hermite–Hadamard inequality for harmonically convex functions via fractional integrals

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  • Chen, Feixiang

Abstract

The main aim of this paper is to give extensions of the Hermite–Hadamard inequality for harmonically convex functions via Riemann–Liouville fractional integrals. We show how to relax the harmonically convexity property of the function f. Obtained results in this work involve a larger class of functions. Our results are the refinements of the existing results for harmonically convex functions.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:apmaco:v:268:y:2015:i:c:p:121-128
    DOI: 10.1016/j.amc.2015.06.051
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    Cited by:

    1. Yahya Almalki & Waqar Afzal, 2023. "Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr - h -Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings," Mathematics, MDPI, vol. 11(19), pages 1-21, September.
    2. Muhammad Bilal Khan & Gustavo Santos-García & Hatim Ghazi Zaini & Savin Treanță & Mohamed S. Soliman, 2022. "Some New Concepts Related to Integral Operators and Inequalities on Coordinates in Fuzzy Fractional Calculus," Mathematics, MDPI, vol. 10(4), pages 1-26, February.
    3. Fangfang Shi & Guoju Ye & Dafang Zhao & Wei Liu, 2020. "Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions," Mathematics, MDPI, vol. 8(4), pages 1-10, April.
    4. 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.
    5. Asfand Fahad & Ayesha & Yuanheng Wang & Saad Ihsaan Butt, 2023. "Jensen–Mercer and Hermite–Hadamard–Mercer Type Inequalities for GA- h -Convex Functions and Its Subclasses with Applications," Mathematics, MDPI, vol. 11(2), pages 1-21, January.

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