Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball
We propose a new concept of set convergence in a Hadamard space and obtain its equivalent condition by using the notion of metric projections. Applying this result, we also prove a convergence theorem for an iterative scheme by the shrinking projection method in a real Hilbert ball.
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| Format: | Article |
| Language: | English |
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Wiley
2010-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2010/582475 |
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| _version_ | 1850164902113574912 |
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| author | Yasunori Kimura |
| author_facet | Yasunori Kimura |
| author_sort | Yasunori Kimura |
| collection | DOAJ |
| description | We propose a new concept of set convergence in a Hadamard space and obtain its equivalent condition by using the notion of metric projections. Applying this result, we also prove a convergence theorem for an iterative scheme by the shrinking projection method in a real Hilbert ball. |
| format | Article |
| id | doaj-art-f16a08ccb9ae4e49ad53dfd1d104d7a4 |
| institution | OA Journals |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2010-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-f16a08ccb9ae4e49ad53dfd1d104d7a42025-08-20T02:21:52ZengWileyAbstract and Applied Analysis1085-33751687-04092010-01-01201010.1155/2010/582475582475Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert BallYasunori Kimura0Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Tokyo 152-8552, JapanWe propose a new concept of set convergence in a Hadamard space and obtain its equivalent condition by using the notion of metric projections. Applying this result, we also prove a convergence theorem for an iterative scheme by the shrinking projection method in a real Hilbert ball.http://dx.doi.org/10.1155/2010/582475 |
| spellingShingle | Yasunori Kimura Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball Abstract and Applied Analysis |
| title | Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball |
| title_full | Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball |
| title_fullStr | Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball |
| title_full_unstemmed | Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball |
| title_short | Convergence of a Sequence of Sets in a Hadamard Space and the Shrinking Projection Method for a Real Hilbert Ball |
| title_sort | convergence of a sequence of sets in a hadamard space and the shrinking projection method for a real hilbert ball |
| url | http://dx.doi.org/10.1155/2010/582475 |
| work_keys_str_mv | AT yasunorikimura convergenceofasequenceofsetsinahadamardspaceandtheshrinkingprojectionmethodforarealhilbertball |