Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces
The purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping xn+1=λnxn+(1−λn)(Txn+en)&...
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| Format: | Article |
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SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://dx.doi.org/10.1155/2010/734181 |
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doaj-bee71fb64d8048c1800742678345faca2020-11-25T02:57:43ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-01201010.1155/2010/734181Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach SpacesL. C. CengY. C. LiouJ. C. YaoThe purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping xn+1=λnxn+(1−λn)(Txn+en)−λnμnF(xn) remains convergent in a Banach space setting where λn,μn∈[0,1], T a nonexpansive mapping, en, n=0,1,…, errors and F a strongly accretive and strictly pseudocontractive mapping. http://dx.doi.org/10.1155/2010/734181 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
L. C. Ceng Y. C. Liou J. C. Yao |
| spellingShingle |
L. C. Ceng Y. C. Liou J. C. Yao Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces Fixed Point Theory and Applications |
| author_facet |
L. C. Ceng Y. C. Liou J. C. Yao |
| author_sort |
L. C. Ceng |
| title |
Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces |
| title_short |
Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces |
| title_full |
Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces |
| title_fullStr |
Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed |
Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces |
| title_sort |
robustness of mann type algorithm with perturbed mapping for nonexpansive mappings in banach spaces |
| publisher |
SpringerOpen |
| series |
Fixed Point Theory and Applications |
| issn |
1687-1820 1687-1812 |
| publishDate |
2010-01-01 |
| description |
The purpose of this paper is to study the robustness of Mann type algorithm in the sense that approximately perturbed mapping does not alter the convergence of Mann type algorithm. It is proven that Mann type algorithm with perturbed mapping xn+1=λnxn+(1−λn)(Txn+en)−λnμnF(xn) remains convergent in a Banach space setting where λn,μn∈[0,1], T a nonexpansive mapping, en, n=0,1,…, errors and F a strongly accretive and strictly pseudocontractive mapping. |
| url |
http://dx.doi.org/10.1155/2010/734181 |
| work_keys_str_mv |
AT lcceng robustnessofmanntypealgorithmwithperturbedmappingfornonexpansivemappingsinbanachspaces AT ycliou robustnessofmanntypealgorithmwithperturbedmappingfornonexpansivemappingsinbanachspaces AT jcyao robustnessofmanntypealgorithmwithperturbedmappingfornonexpansivemappingsinbanachspaces |
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1715342357288714240 |