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Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions

Author

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  • Aqeel Ahmad Mughal
  • Hassan Almusawa
  • Absar Ul Haq
  • Imran Abbas Baloch
  • Ahmet Ocak Akdemir

Abstract

Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as Jensen-type inequality for harmonic h-convex functions. In this paper, we aim to establish the functional form of inequalities presented by Baloch et al. and prove the superadditivity and monotonicity properties of these functionals. Furthermore, we derive the bound for these functionals under certain conditions. Furthermore, we define more generalized functionals involving monotonic nondecreasing concave function as well as evince superadditivity and monotonicity properties of these generalized functionals.

Suggested Citation

  • Aqeel Ahmad Mughal & Hassan Almusawa & Absar Ul Haq & Imran Abbas Baloch & Ahmet Ocak Akdemir, 2021. "Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions," Journal of Mathematics, Hindawi, vol. 2021, pages 1-13, August.
    • Handle: RePEc:hin:jjmath:5561611
    DOI: 10.1155/2021/5561611
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    Cited by:

    1. Waqar Afzal & Mujahid Abbas & Omar Mutab Alsalami, 2024. "Bounds of Different Integral Operators in Tensorial Hilbert and Variable Exponent Function Spaces," Mathematics, MDPI, vol. 12(16), pages 1-33, August.

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