New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations
In this paper, we prove that the solvability of dynamic equations of second order is sufficient for the validity of some Hardy and Opial type inequalities with two different weights on time scales. In particular, the results give new characterizations of two different weights in inequalities contain...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2019/6757080 |
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| author | S. H. Saker A. G. Sayed A. Sikorska-Nowak I. Abohela |
| author_facet | S. H. Saker A. G. Sayed A. Sikorska-Nowak I. Abohela |
| author_sort | S. H. Saker |
| collection | DOAJ |
| description | In this paper, we prove that the solvability of dynamic equations of second order is sufficient for the validity of some Hardy and Opial type inequalities with two different weights on time scales. In particular, the results give new characterizations of two different weights in inequalities containing Hardy and Opial operators. The main contribution in this paper is the characterizations of weights in discrete inequalities that will be formulated from our results as special cases. |
| format | Article |
| id | doaj-art-a15c647c34974ed9a767a315eff274d4 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-a15c647c34974ed9a767a315eff274d42025-02-03T01:11:29ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2019-01-01201910.1155/2019/67570806757080New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic EquationsS. H. Saker0A. G. Sayed1A. Sikorska-Nowak2I. Abohela3Department of Mathematics, Faculty of Science, Mansoura University, Mansoura 35516, EgyptDepartment of Mathematics, Faculty of Science, Al-Azhar University, Nasr City 11884, EgyptFaculty of Mathematics and Computer Science, Adam Mickiewicz University, Uniwersytetu Poznańskiego 4, 61-614 Poznań, PolandCollege of Engineering, Applied Science University, BahrainIn this paper, we prove that the solvability of dynamic equations of second order is sufficient for the validity of some Hardy and Opial type inequalities with two different weights on time scales. In particular, the results give new characterizations of two different weights in inequalities containing Hardy and Opial operators. The main contribution in this paper is the characterizations of weights in discrete inequalities that will be formulated from our results as special cases.http://dx.doi.org/10.1155/2019/6757080 |
| spellingShingle | S. H. Saker A. G. Sayed A. Sikorska-Nowak I. Abohela New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations Discrete Dynamics in Nature and Society |
| title | New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations |
| title_full | New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations |
| title_fullStr | New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations |
| title_full_unstemmed | New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations |
| title_short | New Characterizations of Weights in Hardy and Opial Type Inequalities via Solvability of Dynamic Equations |
| title_sort | new characterizations of weights in hardy and opial type inequalities via solvability of dynamic equations |
| url | http://dx.doi.org/10.1155/2019/6757080 |
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