Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces
Let be a real reflexive Banach space with a weakly continuous duality mapping . Let be a nonempty weakly closed star-shaped (with respect to ) subset of . Let = be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of , which is uniformly continuous at zero. We will sh...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/202095 |
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| author | D. R. Sahu Ngai-Ching Wong Jen-Chih Yao |
| author_facet | D. R. Sahu Ngai-Ching Wong Jen-Chih Yao |
| author_sort | D. R. Sahu |
| collection | DOAJ |
| description | Let be a real reflexive Banach space with a weakly continuous duality mapping . Let be a nonempty weakly closed star-shaped (with respect to ) subset of . Let = be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of , which is uniformly continuous at zero. We will show that the implicit
iteration scheme: , for all , converges strongly to a common fixed point of the semigroup for some suitably chosen
parameters and . Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009). |
| format | Article |
| id | doaj-art-fb19a1d65989446ea0b0be1c582e6f44 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-fb19a1d65989446ea0b0be1c582e6f442025-08-20T03:25:56ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/202095202095Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach SpacesD. R. Sahu0Ngai-Ching Wong1Jen-Chih Yao2Department of Mathematics, Banaras Hindu University, Varanasi 221005, IndiaDepartment of Applied Mathematics, National Sun Yat-Sen University, Kaohsiung 804, TaiwanCenter for Fundamental Science, Kaohsiung Medical University, Kaohsiung 807, TaiwanLet be a real reflexive Banach space with a weakly continuous duality mapping . Let be a nonempty weakly closed star-shaped (with respect to ) subset of . Let = be a uniformly continuous semigroup of asymptotically nonexpansive self-mappings of , which is uniformly continuous at zero. We will show that the implicit iteration scheme: , for all , converges strongly to a common fixed point of the semigroup for some suitably chosen parameters and . Our results extend and improve corresponding ones of Suzuki (2002), Xu (2005), and Zegeye and Shahzad (2009).http://dx.doi.org/10.1155/2013/202095 |
| spellingShingle | D. R. Sahu Ngai-Ching Wong Jen-Chih Yao Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces Abstract and Applied Analysis |
| title | Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_full | Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_fullStr | Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_short | Strong Convergence Theorems for Semigroups of Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_sort | strong convergence theorems for semigroups of asymptotically nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2013/202095 |
| work_keys_str_mv | AT drsahu strongconvergencetheoremsforsemigroupsofasymptoticallynonexpansivemappingsinbanachspaces AT ngaichingwong strongconvergencetheoremsforsemigroupsofasymptoticallynonexpansivemappingsinbanachspaces AT jenchihyao strongconvergencetheoremsforsemigroupsofasymptoticallynonexpansivemappingsinbanachspaces |