Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces
We study descent-like approximation methods and proximal methods of the retraction type for solving fixed-point problems with nonself-mappings in Hilbert and Banach spaces. We prove strong and weak convergences for weakly contractive and nonexpansive maps, respectively. We also establish the stabili...
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| Format: | Article |
| Language: | English |
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Wiley
2003-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337503203018 |
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| _version_ | 1832567563425415168 |
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| author | Yakov Alber Simeon Reich Jen-Chih Yao |
| author_facet | Yakov Alber Simeon Reich Jen-Chih Yao |
| author_sort | Yakov Alber |
| collection | DOAJ |
| description | We study descent-like approximation methods and proximal methods of the retraction type for solving fixed-point problems with
nonself-mappings in Hilbert and Banach spaces. We prove strong
and weak convergences for weakly contractive and nonexpansive
maps, respectively. We also establish the stability of these
methods with respect to perturbations of the operators and the
constraint sets. |
| format | Article |
| id | doaj-art-0a53e69827a44a3596d1dca8fb8f432b |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2003-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-0a53e69827a44a3596d1dca8fb8f432b2025-02-03T01:01:12ZengWileyAbstract and Applied Analysis1085-33751687-04092003-01-012003419321610.1155/S1085337503203018Iterative methods for solving fixed-point problems with nonself-mappings in Banach spacesYakov Alber0Simeon Reich1Jen-Chih Yao2Department of Mathematics, The Technion - Israel Institute of Technology, Haifa 32000, IsraelDepartment of Mathematics, The Technion - Israel Institute of Technology, Haifa 32000, IsraelDepartment of Applied Mathematics, National Sun Yat-sen University, Kaohsiung 804 , TaiwanWe study descent-like approximation methods and proximal methods of the retraction type for solving fixed-point problems with nonself-mappings in Hilbert and Banach spaces. We prove strong and weak convergences for weakly contractive and nonexpansive maps, respectively. We also establish the stability of these methods with respect to perturbations of the operators and the constraint sets.http://dx.doi.org/10.1155/S1085337503203018 |
| spellingShingle | Yakov Alber Simeon Reich Jen-Chih Yao Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces Abstract and Applied Analysis |
| title | Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces |
| title_full | Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces |
| title_fullStr | Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces |
| title_full_unstemmed | Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces |
| title_short | Iterative methods for solving fixed-point problems with nonself-mappings in Banach spaces |
| title_sort | iterative methods for solving fixed point problems with nonself mappings in banach spaces |
| url | http://dx.doi.org/10.1155/S1085337503203018 |
| work_keys_str_mv | AT yakovalber iterativemethodsforsolvingfixedpointproblemswithnonselfmappingsinbanachspaces AT simeonreich iterativemethodsforsolvingfixedpointproblemswithnonselfmappingsinbanachspaces AT jenchihyao iterativemethodsforsolvingfixedpointproblemswithnonselfmappingsinbanachspaces |