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Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings

Author

Listed:
  • Xuexiao You

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

  • Muhammad Aamir Ali

    (Jiangsu Key Laboratory for NSLSCS, School of Mathematical Sciences, Nanjing Normal University, Nanjing 210023, China)

  • Hüseyin Budak

    (Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce 81620, Turkey)

  • Jiraporn Reunsumrit

    (Department of Mathematics, Faculty of Applied Science, King Mongkut’s University of Technology North Bangkok, Bangkok 10800, Thailand)

  • Thanin Sitthiwirattham

    (Mathematics Department, Faculty of Science and Technology, Suan Dusit University, Bangkok 10300, Thailand)

Abstract

In this paper, we prove Hermite–Hadamard–Mercer inequalities, which is a new version of the Hermite–Hadamard inequalities for harmonically convex functions. We also prove Hermite–Hadamard–Mercer-type inequalities for functions whose first derivatives in absolute value are harmonically convex. Finally, we discuss how special means can be used to address newly discovered inequalities.

Suggested Citation

  • Xuexiao You & Muhammad Aamir Ali & Hüseyin Budak & Jiraporn Reunsumrit & Thanin Sitthiwirattham, 2021. "Hermite–Hadamard–Mercer-Type Inequalities for Harmonically Convex Mappings," Mathematics, MDPI, vol. 9(20), pages 1-11, October.
    • Handle: RePEc:gam:jmathe:v:9:y:2021:i:20:p:2556-:d:654260
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    References listed on IDEAS

    as
    1. Imran Abbas Baloch & İmdat İşcan, 2015. "Some Ostrowski Type Inequalities for Harmonically -Convex Functions in Second Sense," International Journal of Analysis, Hindawi, vol. 2015, pages 1-9, October.
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    Cited by:

    1. Vuk Stojiljković & Rajagopalan Ramaswamy & Ola A. Ashour Abdelnaby & Stojan Radenović, 2022. "Riemann-Liouville Fractional Inclusions for Convex Functions Using Interval Valued Setting," Mathematics, MDPI, vol. 10(19), pages 1-16, September.

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