Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces
The purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of nonexpansive mappings in infinite-dimen...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2014-01-01
|
| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2014/943753 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832567055755247616 |
|---|---|
| author | Yanlai Song Luchuan Ceng |
| author_facet | Yanlai Song Luchuan Ceng |
| author_sort | Yanlai Song |
| collection | DOAJ |
| description | The purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of nonexpansive mappings in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating this common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in the very recent literature. |
| format | Article |
| id | doaj-art-baebd1fb192e4f1394d149faad99bd76 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2014-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-baebd1fb192e4f1394d149faad99bd762025-02-03T01:02:30ZengWileyJournal of Applied Mathematics1110-757X1687-00422014-01-01201410.1155/2014/943753943753Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach SpacesYanlai Song0Luchuan Ceng1Department of Mathematics, Shanghai Normal University, Shanghai 200234, ChinaDepartment of Mathematics, Shanghai Normal University, Scientific Computing Key Laboratory of Shanghai University, Shanghai 200234, ChinaThe purpose of this paper is to present two new forward-backward splitting schemes with relaxations and errors for finding a common element of the set of solutions to the variational inclusion problem with two accretive operators and the set of fixed points of nonexpansive mappings in infinite-dimensional Banach spaces. Under mild conditions, some weak and strong convergence theorems for approximating this common elements are proved. The methods in the paper are novel and different from those in the early and recent literature. Our results can be viewed as the improvement, supplementation, development, and extension of the corresponding results in the very recent literature.http://dx.doi.org/10.1155/2014/943753 |
| spellingShingle | Yanlai Song Luchuan Ceng Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces Journal of Applied Mathematics |
| title | Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces |
| title_full | Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces |
| title_fullStr | Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces |
| title_full_unstemmed | Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces |
| title_short | Weak and Strong Convergence Theorems for Zeroes of Accretive Operators in Banach Spaces |
| title_sort | weak and strong convergence theorems for zeroes of accretive operators in banach spaces |
| url | http://dx.doi.org/10.1155/2014/943753 |
| work_keys_str_mv | AT yanlaisong weakandstrongconvergencetheoremsforzeroesofaccretiveoperatorsinbanachspaces AT luchuanceng weakandstrongconvergencetheoremsforzeroesofaccretiveoperatorsinbanachspaces |