Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings
We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2009-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2009/297565 |
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| _version_ | 1832568271437561856 |
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| author | Watcharaporn Cholamjiak Suthep Suantai |
| author_facet | Watcharaporn Cholamjiak Suthep Suantai |
| author_sort | Watcharaporn Cholamjiak |
| collection | DOAJ |
| description | We prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003). |
| format | Article |
| id | doaj-art-1dc8972657d146c28a9e4c8a9ab32e11 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2009-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-1dc8972657d146c28a9e4c8a9ab32e112025-02-03T00:59:19ZengWileyAbstract and Applied Analysis1085-33751687-04092009-01-01200910.1155/2009/297565297565Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive MappingsWatcharaporn Cholamjiak0Suthep Suantai1Department of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandDepartment of Mathematics, Faculty of Science, Chiang Mai University, Chiang Mai 50200, ThailandWe prove a weak convergence theorem of the modified Mann iteration process for a uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mapping in a uniformly convex Banach space. We also introduce two kinds of new monotone hybrid methods and obtain strong convergence theorems for an infinitely countable family of uniformly Lipschitzian and generalized asymptotically quasi-nonexpansive mappings in a Hilbert space. The results improve and extend the corresponding ones announced by Kim and Xu (2006) and Nakajo and Takahashi (2003).http://dx.doi.org/10.1155/2009/297565 |
| spellingShingle | Watcharaporn Cholamjiak Suthep Suantai Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings Abstract and Applied Analysis |
| title | Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings |
| title_full | Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings |
| title_fullStr | Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings |
| title_full_unstemmed | Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings |
| title_short | Monotone Hybrid Projection Algorithms for an Infinitely Countable Family of Lipschitz Generalized Asymptotically Quasi-Nonexpansive Mappings |
| title_sort | monotone hybrid projection algorithms for an infinitely countable family of lipschitz generalized asymptotically quasi nonexpansive mappings |
| url | http://dx.doi.org/10.1155/2009/297565 |
| work_keys_str_mv | AT watcharaporncholamjiak monotonehybridprojectionalgorithmsforaninfinitelycountablefamilyoflipschitzgeneralizedasymptoticallyquasinonexpansivemappings AT suthepsuantai monotonehybridprojectionalgorithmsforaninfinitelycountablefamilyoflipschitzgeneralizedasymptoticallyquasinonexpansivemappings |