On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings
<p/> <p>We prove that the set of common fixed points of a given countable family of relatively nonexpansive mappings is identical to the fixed-point set of a single strongly relatively nonexpansive mapping. This answers Kohsaka and Takahashi's question in positive. We also introduce...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/414232 |
| _version_ | 1818718432589250560 |
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| author | Saejung Satit Nilsrakoo Weerayuth |
| author_facet | Saejung Satit Nilsrakoo Weerayuth |
| author_sort | Saejung Satit |
| collection | DOAJ |
| description | <p/> <p>We prove that the set of common fixed points of a given countable family of relatively nonexpansive mappings is identical to the fixed-point set of a single strongly relatively nonexpansive mapping. This answers Kohsaka and Takahashi's question in positive. We also introduce the concept of strongly generalized nonexpansive mappings and prove the analogue version of the result above for Ibaraki-Takahashi's generalized nonexpansive mappings. The duality theorem for two classes of strongly relatively nonexpansive mappings and of strongly generalized nonexpansive mappings is proved.</p> |
| first_indexed | 2024-12-17T19:50:57Z |
| format | Article |
| id | doaj.art-307aa836de9247f4aa2d9421573d4530 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-17T19:50:57Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-307aa836de9247f4aa2d9421573d45302022-12-21T21:34:43ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101414232On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive MappingsSaejung SatitNilsrakoo Weerayuth<p/> <p>We prove that the set of common fixed points of a given countable family of relatively nonexpansive mappings is identical to the fixed-point set of a single strongly relatively nonexpansive mapping. This answers Kohsaka and Takahashi's question in positive. We also introduce the concept of strongly generalized nonexpansive mappings and prove the analogue version of the result above for Ibaraki-Takahashi's generalized nonexpansive mappings. The duality theorem for two classes of strongly relatively nonexpansive mappings and of strongly generalized nonexpansive mappings is proved.</p>http://www.fixedpointtheoryandapplications.com/content/2010/414232 |
| spellingShingle | Saejung Satit Nilsrakoo Weerayuth On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings Fixed Point Theory and Applications |
| title | On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings |
| title_full | On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings |
| title_fullStr | On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings |
| title_full_unstemmed | On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings |
| title_short | On the Fixed-Point Set of a Family of Relatively Nonexpansive and Generalized Nonexpansive Mappings |
| title_sort | on the fixed point set of a family of relatively nonexpansive and generalized nonexpansive mappings |
| url | http://www.fixedpointtheoryandapplications.com/content/2010/414232 |
| work_keys_str_mv | AT saejungsatit onthefixedpointsetofafamilyofrelativelynonexpansiveandgeneralizednonexpansivemappings AT nilsrakooweerayuth onthefixedpointsetofafamilyofrelativelynonexpansiveandgeneralizednonexpansivemappings |