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

Author:

Zakarya M.12ORCID,AlNemer Ghada3ORCID,Abd El-Hamid H. A.4,Butush Roqia5,Rezk H. M.6ORCID

Affiliation:

1. King Khalid University, College of Science, Department of Mathematics, P.O. Box 9004, 61413 Abha, Saudi Arabia

2. Department of Mathematics, Faculty of Science, Al-Azhar University, 71524 Assiut, Egypt

3. Department of Mathematical Science, College of Science, Princess Nourah bint Abdulrahman University, P.O. Box 84428, Riyadh 11671, Saudi Arabia

4. Department of Mathematics and Computer Science, Faculty of Science, Beni-Suef University, Beni-Suef, Egypt

5. Department of Mathematics, University of Jordan, P.O. Box 11941, Amman, Jordan

6. Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, Egypt

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.

Funder

Princess Nourah Bint Abdulrahman University

Publisher

Hindawi Limited

Subject

General Mathematics

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