Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces
<p/> <p>Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed p...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2007-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2007/021972 |
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doaj-7945392063ea466ea4e3b91aa15b5dd42020-11-25T02:46:33ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122007-01-0120071021972Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach SpacesTakahashi WataruKohsaka Fumiaki<p/> <p>Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.</p> http://www.fixedpointtheoryandapplications.com/content/2007/021972 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Takahashi Wataru Kohsaka Fumiaki |
| spellingShingle |
Takahashi Wataru Kohsaka Fumiaki Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces Fixed Point Theory and Applications |
| author_facet |
Takahashi Wataru Kohsaka Fumiaki |
| author_sort |
Takahashi Wataru |
| title |
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces |
| title_short |
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces |
| title_full |
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces |
| title_fullStr |
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed |
Block Iterative Methods for a Finite Family of Relatively Nonexpansive Mappings in Banach Spaces |
| title_sort |
block iterative methods for a finite family of relatively nonexpansive mappings in banach spaces |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2007-01-01 |
| description |
<p/> <p>Using the convex combination based on Bregman distances due to Censor and Reich, we define an operator from a given family of relatively nonexpansive mappings in a Banach space. We first prove that the fixed-point set of this operator is identical to the set of all common fixed points of the mappings. Next, using this operator, we construct an iterative sequence to approximate common fixed points of the family. We finally apply our results to a convex feasibility problem in Banach spaces.</p> |
| url |
http://www.fixedpointtheoryandapplications.com/content/2007/021972 |
| work_keys_str_mv |
AT takahashiwataru blockiterativemethodsforafinitefamilyofrelativelynonexpansivemappingsinbanachspaces AT kohsakafumiaki blockiterativemethodsforafinitefamilyofrelativelynonexpansivemappingsinbanachspaces |
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1724757704061222912 |