Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings
We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain...
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| Format: | Article |
| Language: | English |
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Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/573156 |
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| _version_ | 1832550549299396608 |
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| author | Jong Soo Jung |
| author_facet | Jong Soo Jung |
| author_sort | Jong Soo Jung |
| collection | DOAJ |
| description | We propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings
in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative
scheme to a solution of a ceratin variational inequality is established. |
| format | Article |
| id | doaj-art-4a845b59aa434688badbf6749328f3fa |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-4a845b59aa434688badbf6749328f3fa2025-02-03T06:06:24ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/573156573156Strong Convergence of Viscosity Iteration Methods for Nonexpansive MappingsJong Soo Jung0Department of Mathematics, Dong-A University, Busan 604-714, South KoreaWe propose a new viscosity iterative scheme for finding fixed points of nonexpansive mappings in a reflexive Banach space having a uniformly Gâteaux differentiable norm and satisfying that every weakly compact convex subset of the space has the fixed point property for nonexpansive mappings. Certain different control conditions for viscosity iterative scheme are given and strong convergence of viscosity iterative scheme to a solution of a ceratin variational inequality is established.http://dx.doi.org/10.1155/2009/573156 |
| spellingShingle | Jong Soo Jung Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings Abstract and Applied Analysis |
| title | Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings |
| title_full | Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings |
| title_fullStr | Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings |
| title_full_unstemmed | Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings |
| title_short | Strong Convergence of Viscosity Iteration Methods for Nonexpansive Mappings |
| title_sort | strong convergence of viscosity iteration methods for nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2009/573156 |
| work_keys_str_mv | AT jongsoojung strongconvergenceofviscosityiterationmethodsfornonexpansivemappings |