Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings
We introduce two general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach space. Under suitable setting, we not only obtain several convergence theorems announced by many authors but also prove them under weaker assumptions. App...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2010-01-01
|
| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/407651 |
| _version_ | 1798029248515014656 |
|---|---|
| author | Daruni Boonchari Satit Saejung |
| author_facet | Daruni Boonchari Satit Saejung |
| author_sort | Daruni Boonchari |
| collection | DOAJ |
| description | We introduce two general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach space. Under suitable setting, we not only obtain several convergence theorems announced by many authors but also prove them under weaker assumptions. Applications to the problem of finding a common element of the fixed point set of a relatively nonexpansive mapping and the solution set of an equilibrium problem are also discussed. |
| first_indexed | 2024-04-11T19:22:16Z |
| format | Article |
| id | doaj.art-772cacecc84b4658a88c2e328b29a440 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-04-11T19:22:16Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-772cacecc84b4658a88c2e328b29a4402022-12-22T04:07:17ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-01201010.1155/2010/407651Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive MappingsDaruni BoonchariSatit SaejungWe introduce two general iterative schemes for finding a common fixed point of a countable family of relatively nonexpansive mappings in a Banach space. Under suitable setting, we not only obtain several convergence theorems announced by many authors but also prove them under weaker assumptions. Applications to the problem of finding a common element of the fixed point set of a relatively nonexpansive mapping and the solution set of an equilibrium problem are also discussed.http://dx.doi.org/10.1155/2010/407651 |
| spellingShingle | Daruni Boonchari Satit Saejung Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings Fixed Point Theory and Applications |
| title | Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings |
| title_full | Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings |
| title_fullStr | Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings |
| title_full_unstemmed | Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings |
| title_short | Approximation of Common Fixed Points of a Countable Family of Relatively Nonexpansive Mappings |
| title_sort | approximation of common fixed points of a countable family of relatively nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2010/407651 |
| work_keys_str_mv | AT daruniboonchari approximationofcommonfixedpointsofacountablefamilyofrelativelynonexpansivemappings AT satitsaejung approximationofcommonfixedpointsofacountablefamilyofrelativelynonexpansivemappings |