The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping
The purpose of this paper is to prove, by asymptotic center techniques and the methods of Hilbert spaces, the following theorem. Let H be a Hilbert space, let C be a nonempty bounded closed convex subset of H, and let M=[an,k]n,k≥1 be a strongly ergodic matrix. If T:C→C is a li...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2009-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2009/586487 |
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doaj-19c5af6b05fb4723994a7285bfe4164a2020-11-24T21:54:00ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122009-01-01200910.1155/2009/586487The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian MappingJaros&#322;aw G&#243;rnickiThe purpose of this paper is to prove, by asymptotic center techniques and the methods of Hilbert spaces, the following theorem. Let H be a Hilbert space, let C be a nonempty bounded closed convex subset of H, and let M=[an,k]n,k≥1 be a strongly ergodic matrix. If T:C→C is a lipschitzian mapping such that lim⁡inf⁡n→∞inf⁡m=0,1,...∑k=1∞an,k·‖Tk+m‖2<2, then the set of fixed points Fix T={x∈C:Tx=x} is a retract of C. This result extends and improves the corresponding results of [7, Corollary 9] and [8, Corollary 1]. http://dx.doi.org/10.1155/2009/586487 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Jaros&#322;aw G&#243;rnicki |
| spellingShingle |
Jaros&#322;aw G&#243;rnicki The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping Fixed Point Theory and Applications |
| author_facet |
Jaros&#322;aw G&#243;rnicki |
| author_sort |
Jaros&#322;aw G&#243;rnicki |
| title |
The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping |
| title_short |
The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping |
| title_full |
The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping |
| title_fullStr |
The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping |
| title_full_unstemmed |
The Methods of Hilbert Spaces and Structure of the Fixed-Point Set of Lipschitzian Mapping |
| title_sort |
methods of hilbert spaces and structure of the fixed-point set of lipschitzian mapping |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2009-01-01 |
| description |
The purpose of this paper is to prove, by asymptotic center techniques and the methods of Hilbert spaces, the following theorem. Let H be a Hilbert space, let C be a nonempty bounded closed convex subset of H, and let M=[an,k]n,k≥1 be a strongly ergodic matrix. If T:C→C is a lipschitzian mapping such that lim⁡inf⁡n→∞inf⁡m=0,1,...∑k=1∞an,k·‖Tk+m‖2<2, then the set of fixed points Fix T={x∈C:Tx=x} is a retract of C. This result extends and improves the corresponding results of [7, Corollary 9] and [8, Corollary 1]. |
| url |
http://dx.doi.org/10.1155/2009/586487 |
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AT jarosamp322awgamp243rnicki themethodsofhilbertspacesandstructureofthefixedpointsetoflipschitzianmapping AT jarosamp322awgamp243rnicki methodsofhilbertspacesandstructureofthefixedpointsetoflipschitzianmapping |
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