Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces
In 1965, Kirk proved that if C is a nonempty weakly compact convex subset of a Banach space with normal structure, then every nonexpansive mapping T:C→C has a fixed point. The purpose of this paper is to outline various generalizations of Kirk's fixed point theorem to semigroup of...
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SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/580956 |
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doaj-eb31cee3ac3242bca3cd20a246e0c58a2020-11-24T21:40:08ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-01201010.1155/2010/580956Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach SpacesAnthony To-Ming LauIn 1965, Kirk proved that if C is a nonempty weakly compact convex subset of a Banach space with normal structure, then every nonexpansive mapping T:C→C has a fixed point. The purpose of this paper is to outline various generalizations of Kirk's fixed point theorem to semigroup of nonexpansive mappings and for Banach spaces associated to a locally compact group. http://dx.doi.org/10.1155/2010/580956 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Anthony To-Ming Lau |
| spellingShingle |
Anthony To-Ming Lau Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces Fixed Point Theory and Applications |
| author_facet |
Anthony To-Ming Lau |
| author_sort |
Anthony To-Ming Lau |
| title |
Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces |
| title_short |
Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces |
| title_full |
Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces |
| title_fullStr |
Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed |
Normal Structure and Common Fixed Point Properties for Semigroups of Nonexpansive Mappings in Banach Spaces |
| title_sort |
normal structure and common fixed point properties for semigroups of nonexpansive mappings in banach spaces |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2010-01-01 |
| description |
In 1965, Kirk proved that if C is a nonempty weakly compact convex subset of a Banach space with normal structure, then every nonexpansive mapping T:C→C has a fixed point. The purpose of this paper is to outline various generalizations of Kirk's fixed point theorem to semigroup of nonexpansive mappings and for Banach spaces associated to a locally compact group. |
| url |
http://dx.doi.org/10.1155/2010/580956 |
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AT anthonytominglau normalstructureandcommonfixedpointpropertiesforsemigroupsofnonexpansivemappingsinbanachspaces |
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1716670571654152192 |