Generalizations of integral inequalities similar to Hardy inequality on time scales

Volume 32, Issue 3, pp 241--256 http://dx.doi.org/10.22436/jmcs.032.03.05

Publication Date: September 29, 2023 Submission Date: January 01, 2023 Revision Date: May 13, 2023 Accteptance Date: August 02, 2023

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Authors

W. M. Hasan - Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt. H. M. El-Owaidy - Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt. A. A. El-Deeb - Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt. H. M. Rezk - Department of Mathematics, Faculty of Science, Al-Azhar University, Nasr City (11884), Cairo, Egypt.

Abstract

In this article, we prove some new inequalities similar to Hardy's inequality on time scales. The results as special cases contain integral inequalities similar to Hardy's inequality and contain discrete inequalities. Our main results are established by using chain rule, Holder inequality, and some properties of multiple integrals on time scales. Furthermore, some applications and examples are given to illustrate the investigated results.

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Keywords

• Time scales
• dynamic inequality
• Hardy's inequality

MSC

•  26D15
•  26E70

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