Some new generalized weighted dynamic inequalities of Hardy's type on time scales

Volume 23, Issue 4, pp 289--301 http://dx.doi.org/10.22436/jmcs.023.04.02

Publication Date: November 22, 2020 Submission Date: August 12, 2020 Revision Date: September 01, 2020 Accteptance Date: October 03, 2020

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Authors

S. H. Saker - Department of Mathematics, Faculty of Science, Mansoura University, Mansoura, Egypt. M. M. A. El-sheikh - Department of Mathematics, Faculty of Science, Menoufia University, Menoufia, Egypt. A. M. Madian - Department of Mathematics, Faculty of Science, Menoufia University, Menoufia, Egypt.

Abstract

In this paper, we will prove some new generalized weighted dynamic inequalities of Hardy's type on a time scale \(\mathbb{T}\). The obtained results contain as special cases some published results when the time scale \( \mathbb{T=R}\) and when \(\mathbb{T=N}.\) The results, to the best of the authors' knowledge, are essentially new.

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Keywords

• Hardy type inequality
• monotonic functions
• time scales
• dynamic inequalities

MSC

•  26D10
•  26D15
•  34N05
•  47B38
•  39A12

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