On Hardy–Knopp Type Inequalities with Kernels via Time Scale Calculus

In this paper, we study the inequalities of Hardy–Knopp type with kernel functions which have two nonnegative different weighted functions in two different spaces, in a general domain called a time scale calculus. A time scale calculus T is considered as a unification of the continuous calculus and...

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Main Authors: H. M. Rezk, A. I. Saied, Ghada AlNemer, M. Zakarya
Format: Article
Language:English
Published: Wiley 2022-01-01
Series:Journal of Mathematics
Online Access:http://dx.doi.org/10.1155/2022/7997299
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author H. M. Rezk
A. I. Saied
Ghada AlNemer
M. Zakarya
author_facet H. M. Rezk
A. I. Saied
Ghada AlNemer
M. Zakarya
author_sort H. M. Rezk
collection DOAJ
description In this paper, we study the inequalities of Hardy–Knopp type with kernel functions which have two nonnegative different weighted functions in two different spaces, in a general domain called a time scale calculus. A time scale calculus T is considered as a unification of the continuous calculus and the discrete calculus. We will prove these inequalities in a time scale calculus to avoid proving them twice once in the continuous case and the second in the discrete case. Also, as special cases of the time scale calculus, we can prove some new inequalities in new different domains. Our results will be proved by using the definition of a general Hardy operator on time scale. These inequalities (when T=ℕ) are essentially new.
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institution Kabale University
issn 2314-4785
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publishDate 2022-01-01
publisher Wiley
record_format Article
series Journal of Mathematics
spelling doaj-art-06c34539316d4b94b462171610ea776e2025-02-03T01:23:35ZengWileyJournal of Mathematics2314-47852022-01-01202210.1155/2022/7997299On Hardy–Knopp Type Inequalities with Kernels via Time Scale CalculusH. M. Rezk0A. I. Saied1Ghada AlNemer2M. Zakarya3Department of MathematicsDepartment of MathematicsDepartment of Mathematical SciencesKing Khalid UniversityIn this paper, we study the inequalities of Hardy–Knopp type with kernel functions which have two nonnegative different weighted functions in two different spaces, in a general domain called a time scale calculus. A time scale calculus T is considered as a unification of the continuous calculus and the discrete calculus. We will prove these inequalities in a time scale calculus to avoid proving them twice once in the continuous case and the second in the discrete case. Also, as special cases of the time scale calculus, we can prove some new inequalities in new different domains. Our results will be proved by using the definition of a general Hardy operator on time scale. These inequalities (when T=ℕ) are essentially new.http://dx.doi.org/10.1155/2022/7997299
spellingShingle H. M. Rezk
A. I. Saied
Ghada AlNemer
M. Zakarya
On Hardy–Knopp Type Inequalities with Kernels via Time Scale Calculus
Journal of Mathematics
title On Hardy–Knopp Type Inequalities with Kernels via Time Scale Calculus
title_full On Hardy–Knopp Type Inequalities with Kernels via Time Scale Calculus
title_fullStr On Hardy–Knopp Type Inequalities with Kernels via Time Scale Calculus
title_full_unstemmed On Hardy–Knopp Type Inequalities with Kernels via Time Scale Calculus
title_short On Hardy–Knopp Type Inequalities with Kernels via Time Scale Calculus
title_sort on hardy knopp type inequalities with kernels via time scale calculus
url http://dx.doi.org/10.1155/2022/7997299
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