The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces
We introduce two general hybrid iterative approximation methods (one implicit and one explicit) for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly positive bounded linear operators. Strong convergence theorems of the proposed iterat...
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| Format: | Article |
| Language: | English |
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Wiley
2011-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2011/854360 |
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| _version_ | 1832548147172212736 |
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| author | Rabian Wangkeeree |
| author_facet | Rabian Wangkeeree |
| author_sort | Rabian Wangkeeree |
| collection | DOAJ |
| description | We introduce two general hybrid iterative approximation methods (one implicit and one explicit)
for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly
positive bounded linear operators. Strong convergence theorems of the proposed iterative methods are obtained in a
reflexive Banach space which admits a weakly continuous duality mapping. The results presented in this paper improve
and extend the corresponding results announced by Marino and Xu (2006), Wangkeeree et al. (in press), and Ceng et al. (2009). |
| format | Article |
| id | doaj-art-b5a3d150f8344ecca6f33e8ad16b3fe9 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2011-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-b5a3d150f8344ecca6f33e8ad16b3fe92025-02-03T06:42:04ZengWileyAbstract and Applied Analysis1085-33751687-04092011-01-01201110.1155/2011/854360854360The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach SpacesRabian Wangkeeree0Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandWe introduce two general hybrid iterative approximation methods (one implicit and one explicit) for finding a fixed point of a nonexpansive mapping which solving the variational inequality generated by two strongly positive bounded linear operators. Strong convergence theorems of the proposed iterative methods are obtained in a reflexive Banach space which admits a weakly continuous duality mapping. The results presented in this paper improve and extend the corresponding results announced by Marino and Xu (2006), Wangkeeree et al. (in press), and Ceng et al. (2009).http://dx.doi.org/10.1155/2011/854360 |
| spellingShingle | Rabian Wangkeeree The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces Abstract and Applied Analysis |
| title | The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces |
| title_full | The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces |
| title_fullStr | The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces |
| title_short | The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces |
| title_sort | general hybrid approximation methods for nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2011/854360 |
| work_keys_str_mv | AT rabianwangkeeree thegeneralhybridapproximationmethodsfornonexpansivemappingsinbanachspaces AT rabianwangkeeree generalhybridapproximationmethodsfornonexpansivemappingsinbanachspaces |