The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems
In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical syste...
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| Format: | Article |
| Language: | English |
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Wiley
2004-01-01
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| Series: | Journal of Function Spaces and Applications |
| Online Access: | http://dx.doi.org/10.1155/2004/543714 |
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| _version_ | 1832564801285390336 |
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| author | George Isac Monica G. Cojocaru |
| author_facet | George Isac Monica G. Cojocaru |
| author_sort | George Isac |
| collection | DOAJ |
| description | In the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators. |
| format | Article |
| id | doaj-art-0fe2e7cde1ad4f57af01c6f4884fc46a |
| institution | Kabale University |
| issn | 0972-6802 |
| language | English |
| publishDate | 2004-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Function Spaces and Applications |
| spelling | doaj-art-0fe2e7cde1ad4f57af01c6f4884fc46a2025-02-03T01:10:09ZengWileyJournal of Function Spaces and Applications0972-68022004-01-0121719510.1155/2004/543714The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systemsGeorge Isac0Monica G. Cojocaru1Department of Mathematics, Royal Military College of Canada, P.O. Box 17000 STN Forces, Kingston, Ontario, K7K 7B4, CanadaDepartment of Mathematics and Statistics, Queen's University, Jeffery Hall, Kingston, Ontario, K7L 3N6, CanadaIn the first part of this paper we present a representation theorem for the directional derivative of the metric projection operator in an arbitrary Hilbert space. As a consequence of the representation theorem, we present in the second part the development of the theory of projected dynamical systems in infinite dimensional Hilbert space. We show that this development is possible if we use the viable solutions of differential inclusions. We use also pseudomonotone operators.http://dx.doi.org/10.1155/2004/543714 |
| spellingShingle | George Isac Monica G. Cojocaru The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems Journal of Function Spaces and Applications |
| title | The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems |
| title_full | The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems |
| title_fullStr | The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems |
| title_full_unstemmed | The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems |
| title_short | The projection operator in a Hilbert space and its directional derivative. Consequences for the theory of projected dynamical systems |
| title_sort | projection operator in a hilbert space and its directional derivative consequences for the theory of projected dynamical systems |
| url | http://dx.doi.org/10.1155/2004/543714 |
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