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On Refinements of Multidimensional Inequalities of Hardy-Type via Superquadratic and Subquadratic Functions

Author

Listed:
  • M. Zakarya
  • Ghada AlNemer
  • H. A. Abd El-Hamid
  • Roqia Butush
  • H. M. Rezk
  • Ding-Xuan Zhou

Abstract

By utilizing the peculiarities of superquadratic and subquadratic functions, we give the extensions for multidimensional inequalities of Hardy-type with general kernel. We use some algebraic inequalities such as the Minkowski inequality, the refined Jensen inequality, and the Bernoulli inequality to prove the essential results in this paper. The performance of the superquadratic functions is reliable and effective to obtain new dynamic inequalities on time scales. By utilizing special kernels, we also acquire numerous examples and implementations of the related inequalities.

Suggested Citation

  • M. Zakarya & Ghada AlNemer & H. A. Abd El-Hamid & Roqia Butush & H. M. Rezk & Ding-Xuan Zhou, 2022. "On Refinements of Multidimensional Inequalities of Hardy-Type via Superquadratic and Subquadratic Functions," Journal of Mathematics, Hindawi, vol. 2022, pages 1-17, November.
    • Handle: RePEc:hin:jjmath:7668860
    DOI: 10.1155/2022/7668860
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