A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings
<p>Abstract</p> <p>In the paper by Hu in 2008, the author proved a strong convergence result for nonexpansive mappings using a modified Halpern's iteration algorithm. Unfortunately, the case <inline-formula> <graphic file="1687-1812-2010-805326-i1.gif"/>&...
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| Format: | Article |
| Language: | English |
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SpringerOpen
2010-01-01
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| Series: | Fixed Point Theory and Applications |
| Online Access: | http://www.fixedpointtheoryandapplications.com/content/2010/805326 |
| _version_ | 1818999398104825856 |
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| author | Wang Shuang |
| author_facet | Wang Shuang |
| author_sort | Wang Shuang |
| collection | DOAJ |
| description | <p>Abstract</p> <p>In the paper by Hu in 2008, the author proved a strong convergence result for nonexpansive mappings using a modified Halpern's iteration algorithm. Unfortunately, the case <inline-formula> <graphic file="1687-1812-2010-805326-i1.gif"/></inline-formula> does not guarantee the strong convergence of the sequence <inline-formula> <graphic file="1687-1812-2010-805326-i2.gif"/></inline-formula>. In this note, we provide a counter-example to the theorem.</p> |
| first_indexed | 2024-12-20T22:16:47Z |
| format | Article |
| id | doaj.art-7dd35dfc2603479fb7f303a2902913eb |
| institution | Directory Open Access Journal |
| issn | 1687-1820 1687-1812 |
| language | English |
| last_indexed | 2024-12-20T22:16:47Z |
| publishDate | 2010-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Fixed Point Theory and Applications |
| spelling | doaj.art-7dd35dfc2603479fb7f303a2902913eb2022-12-21T19:25:02ZengSpringerOpenFixed Point Theory and Applications1687-18201687-18122010-01-0120101805326A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive MappingsWang Shuang<p>Abstract</p> <p>In the paper by Hu in 2008, the author proved a strong convergence result for nonexpansive mappings using a modified Halpern's iteration algorithm. Unfortunately, the case <inline-formula> <graphic file="1687-1812-2010-805326-i1.gif"/></inline-formula> does not guarantee the strong convergence of the sequence <inline-formula> <graphic file="1687-1812-2010-805326-i2.gif"/></inline-formula>. In this note, we provide a counter-example to the theorem.</p>http://www.fixedpointtheoryandapplications.com/content/2010/805326 |
| spellingShingle | Wang Shuang A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings Fixed Point Theory and Applications |
| title | A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings |
| title_full | A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings |
| title_fullStr | A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings |
| title_full_unstemmed | A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings |
| title_short | A Note on Strong Convergence of a Modified Halpern's Iteration for Nonexpansive Mappings |
| title_sort | note on strong convergence of a modified halpern s iteration for nonexpansive mappings |
| url | http://www.fixedpointtheoryandapplications.com/content/2010/805326 |
| work_keys_str_mv | AT wangshuang anoteonstrongconvergenceofamodifiedhalpernsiterationfornonexpansivemappings AT wangshuang noteonstrongconvergenceofamodifiedhalpernsiterationfornonexpansivemappings |