Viscosity Approximation of Common Fixed Points for <inline-formula> <graphic file="1029-242X-2009-936121-i1.gif"/></inline-formula>-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces
<p/> <p>We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong converg...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
SpringerOpen
2009-01-01
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| Series: | Journal of Inequalities and Applications |
| Online Access: | http://www.journalofinequalitiesandapplications.com/content/2009/936121 |
| _version_ | 1818992878737686528 |
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| author | Kim JongKyu Li Xue-song Huang Nan-jing |
| author_facet | Kim JongKyu Li Xue-song Huang Nan-jing |
| author_sort | Kim JongKyu |
| collection | DOAJ |
| description | <p/> <p>We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007) and the pseudocontractive mapping in (Zegeye et al., 2007) to the pseudocontractive semigroup in Banach spaces under different conditions.</p> |
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| format | Article |
| id | doaj.art-0f7737eb5c1549dc8e50399b19c3cd7d |
| institution | Directory Open Access Journal |
| issn | 1025-5834 1029-242X |
| language | English |
| last_indexed | 2024-12-20T20:33:10Z |
| publishDate | 2009-01-01 |
| publisher | SpringerOpen |
| record_format | Article |
| series | Journal of Inequalities and Applications |
| spelling | doaj.art-0f7737eb5c1549dc8e50399b19c3cd7d2022-12-21T19:27:18ZengSpringerOpenJournal of Inequalities and Applications1025-58341029-242X2009-01-0120091936121Viscosity Approximation of Common Fixed Points for <inline-formula> <graphic file="1029-242X-2009-936121-i1.gif"/></inline-formula>-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach SpacesKim JongKyuLi Xue-songHuang Nan-jing<p/> <p>We study the strong convergence of two kinds of viscosity iteration processes for approximating common fixed points of the pseudocontractive semigroup in uniformly convex Banach spaces with uniformly Gâteaux differential norms. As special cases, we get the strong convergence of the implicit viscosity iteration process for approximating common fixed points of the nonexpansive semigroup in Banach spaces satisfying some conditions. The results presented in this paper extend and generalize some results concerned with the nonexpansive semigroup in (Chen and He, 2007) and the pseudocontractive mapping in (Zegeye et al., 2007) to the pseudocontractive semigroup in Banach spaces under different conditions.</p>http://www.journalofinequalitiesandapplications.com/content/2009/936121 |
| spellingShingle | Kim JongKyu Li Xue-song Huang Nan-jing Viscosity Approximation of Common Fixed Points for <inline-formula> <graphic file="1029-242X-2009-936121-i1.gif"/></inline-formula>-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces Journal of Inequalities and Applications |
| title | Viscosity Approximation of Common Fixed Points for <inline-formula> <graphic file="1029-242X-2009-936121-i1.gif"/></inline-formula>-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces |
| title_full | Viscosity Approximation of Common Fixed Points for <inline-formula> <graphic file="1029-242X-2009-936121-i1.gif"/></inline-formula>-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces |
| title_fullStr | Viscosity Approximation of Common Fixed Points for <inline-formula> <graphic file="1029-242X-2009-936121-i1.gif"/></inline-formula>-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces |
| title_full_unstemmed | Viscosity Approximation of Common Fixed Points for <inline-formula> <graphic file="1029-242X-2009-936121-i1.gif"/></inline-formula>-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces |
| title_short | Viscosity Approximation of Common Fixed Points for <inline-formula> <graphic file="1029-242X-2009-936121-i1.gif"/></inline-formula>-Lipschitzian Semigroup of Pseudocontractive Mappings in Banach Spaces |
| title_sort | viscosity approximation of common fixed points for inline formula graphic file 1029 242x 2009 936121 i1 gif inline formula lipschitzian semigroup of pseudocontractive mappings in banach spaces |
| url | http://www.journalofinequalitiesandapplications.com/content/2009/936121 |
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