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Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel

Author

Listed:
  • Xia Wu

    (School of Mathematics and Finance, Xiangnan University, Chenzhou 411105, China)

  • JinRong Wang

    (Department of Mathematics, Guizhou University, Guiyang 550025, China
    School of Mathematical Sciences, Qufu Normal University, Qufu 273165, China)

  • Jialu Zhang

    (School of Mathematics and Finance, Xiangnan University, Chenzhou 411105, China)

Abstract

In this paper, we establish three fundamental integral identities by the first- and second-order derivatives for a given function via the fractional integrals with exponential kernel. With the help of these new fractional integral identities, we introduce a few interesting Hermite–Hadamard-type inequalities involving left-sided and right-sided fractional integrals with exponential kernels for convex functions. Finally, some applications to special means of real number are presented.

Suggested Citation

  • Xia Wu & JinRong Wang & Jialu Zhang, 2019. "Hermite–Hadamard-Type Inequalities for Convex Functions via the Fractional Integrals with Exponential Kernel," Mathematics, MDPI, vol. 7(9), pages 1-12, September.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:9:p:845-:d:266802
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    References listed on IDEAS

    as
    1. 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.
    2. 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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    Cited by:

    1. Muhammad Bilal Khan & Jorge E. Macías-Díaz & Savin Treanțǎ & Mohamed S. Soliman, 2022. "Some Fejér-Type Inequalities for Generalized Interval-Valued Convex Functions," Mathematics, MDPI, vol. 10(20), pages 1-16, October.
    2. Peng, Yu & Özcan, Serap & Du, Tingsong, 2024. "Symmetrical Hermite–Hadamard type inequalities stemming from multiplicative fractional integrals," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

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