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Some Fractional Hermite–Hadamard Type Inequalities for Interval-Valued Functions

Author

Listed:
  • 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)

  • Wei Liu

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

Abstract

In this paper, firstly we prove the relationship between interval h -convex functions and interval harmonically h -convex functions. Secondly, several new Hermite–Hadamard type inequalities for interval h -convex functions via interval Riemann–Liouville type fractional integrals are established. Finally, we obtain some new fractional Hadamard–Hermite type inequalities for interval harmonically h -convex functions by using the above relationship. Also we discuss the importance of our results and some special cases. Our results extend and improve some previously known results.

Suggested Citation

  • 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.
    • Handle: RePEc:gam:jmathe:v:8:y:2020:i:4:p:534-:d:341552
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    References listed on IDEAS

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    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. 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.
    4. 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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