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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Hindawi Limited
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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doaj-b5a3d150f8344ecca6f33e8ad16b3fe92020-11-25T00:04:41ZengHindawi LimitedAbstract 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 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Rabian Wangkeeree |
| spellingShingle |
Rabian Wangkeeree The General Hybrid Approximation Methods for Nonexpansive Mappings in Banach Spaces Abstract and Applied Analysis |
| author_facet |
Rabian Wangkeeree |
| author_sort |
Rabian Wangkeeree |
| title |
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_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_sort |
general hybrid approximation methods for nonexpansive mappings in banach spaces |
| publisher |
Hindawi Limited |
| series |
Abstract and Applied Analysis |
| issn |
1085-3375 1687-0409 |
| publishDate |
2011-01-01 |
| 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). |
| url |
http://dx.doi.org/10.1155/2011/854360 |
| work_keys_str_mv |
AT rabianwangkeeree thegeneralhybridapproximationmethodsfornonexpansivemappingsinbanachspaces AT rabianwangkeeree generalhybridapproximationmethodsfornonexpansivemappingsinbanachspaces |
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1725428618076618752 |