Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings
Using the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Our results include many convergence theorems by Xu and Ori (2001) and...
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
|
| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2008/732193 |
| _version_ | 1818580442526253056 |
|---|---|
| author | Satit Saejung Weerayuth Nilsrakoo Kittikorn Nakprasit |
| author_facet | Satit Saejung Weerayuth Nilsrakoo Kittikorn Nakprasit |
| author_sort | Satit Saejung |
| collection | DOAJ |
| description | Using the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Our results include many convergence theorems by Xu and Ori (2001) and Zhang and Su (2007) as special cases. We also apply our method to find a common element to the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem. Finally, we propose an iteration to obtain convergence theorems for a continuous monotone mapping. |
| first_indexed | 2024-12-16T07:17:40Z |
| format | Article |
| id | doaj.art-b07caef08162422c87c8219d2a351905 |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-16T07:17:40Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-b07caef08162422c87c8219d2a3519052022-12-21T22:39:44ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122009-01-01200810.1155/2008/732193Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive MappingsSatit SaejungWeerayuth NilsrakooKittikorn NakprasitUsing the implicit iteration and the hybrid method in mathematical programming, we prove weak and strong convergence theorems for finding common fixed points of a countable family of nonexpansive mappings in a real Hilbert space. Our results include many convergence theorems by Xu and Ori (2001) and Zhang and Su (2007) as special cases. We also apply our method to find a common element to the set of fixed points of a nonexpansive mapping and the set of solutions of an equilibrium problem. Finally, we propose an iteration to obtain convergence theorems for a continuous monotone mapping.http://dx.doi.org/10.1155/2008/732193 |
| spellingShingle | Satit Saejung Weerayuth Nilsrakoo Kittikorn Nakprasit Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings Fixed Point Theory and Applications |
| title | Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings |
| title_full | Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings |
| title_fullStr | Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings |
| title_full_unstemmed | Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings |
| title_short | Weak and Strong Convergence Theorems of an Implicit Iteration Process for a Countable Family of Nonexpansive Mappings |
| title_sort | weak and strong convergence theorems of an implicit iteration process for a countable family of nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2008/732193 |
| work_keys_str_mv | AT satitsaejung weakandstrongconvergencetheoremsofanimplicititerationprocessforacountablefamilyofnonexpansivemappings AT weerayuthnilsrakoo weakandstrongconvergencetheoremsofanimplicititerationprocessforacountablefamilyofnonexpansivemappings AT kittikornnakprasit weakandstrongconvergencetheoremsofanimplicititerationprocessforacountablefamilyofnonexpansivemappings |