Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces
<p/> <p>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 <inline-formula> <graphic fil...
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2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/734181 |
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doaj-7bcc3969344b4f7499f04e4f2e9274942020-11-25T00:26:18ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101734181Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach SpacesYao JCLiou YCCeng LC<p/> <p>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 <inline-formula> <graphic file="1687-1812-2010-734181-i1.gif"/></inline-formula> remains convergent in a Banach space setting where <inline-formula> <graphic file="1687-1812-2010-734181-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2010-734181-i3.gif"/></inline-formula> a nonexpansive mapping, <inline-formula> <graphic file="1687-1812-2010-734181-i4.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2010-734181-i5.gif"/></inline-formula>, errors and <inline-formula> <graphic file="1687-1812-2010-734181-i6.gif"/></inline-formula> a strongly accretive and strictly pseudocontractive mapping.</p>http://www.fixedpointtheoryandapplications.com/content/2010/734181 |
| collection |
DOAJ |
| language |
English |
| format |
Article |
| sources |
DOAJ |
| author |
Yao JC Liou YC Ceng LC |
| spellingShingle |
Yao JC Liou YC Ceng LC Robustness of Mann Type Algorithm with Perturbed Mapping for Nonexpansive Mappings in Banach Spaces Fixed Point Theory and Applications |
| author_facet |
Yao JC Liou YC Ceng LC |
| author_sort |
Yao JC |
| 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 |
<p/> <p>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 <inline-formula> <graphic file="1687-1812-2010-734181-i1.gif"/></inline-formula> remains convergent in a Banach space setting where <inline-formula> <graphic file="1687-1812-2010-734181-i2.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2010-734181-i3.gif"/></inline-formula> a nonexpansive mapping, <inline-formula> <graphic file="1687-1812-2010-734181-i4.gif"/></inline-formula>, <inline-formula> <graphic file="1687-1812-2010-734181-i5.gif"/></inline-formula>, errors and <inline-formula> <graphic file="1687-1812-2010-734181-i6.gif"/></inline-formula> a strongly accretive and strictly pseudocontractive mapping.</p> |
| url |
http://www.fixedpointtheoryandapplications.com/content/2010/734181 |
| work_keys_str_mv |
AT yaojc robustnessofmanntypealgorithmwithperturbedmappingfornonexpansivemappingsinbanachspaces AT liouyc robustnessofmanntypealgorithmwithperturbedmappingfornonexpansivemappingsinbanachspaces AT cenglc robustnessofmanntypealgorithmwithperturbedmappingfornonexpansivemappingsinbanachspaces |
| _version_ |
1716170806661218304 |