On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces
We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically I-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by (C. E. Chidume and E. U. Ofo...
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/281383 |
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| author | Farrukh Mukhamedov Mansoor Saburov |
| author_facet | Farrukh Mukhamedov Mansoor Saburov |
| author_sort | Farrukh Mukhamedov |
| collection | DOAJ |
| description | We unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically I-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by (C. E. Chidume and E. U. Ofoedu, 2009). We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family of total asymptotically I-nonexpansive and total asymptotically nonexpansive mappings, defined on a nonempty closed-convex subset of uniformly convex Banach spaces. Moreover, our results extend and unify all known results. |
| format | Article |
| id | doaj-art-9f196793037c4a2c95bf0dae7de92001 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-9f196793037c4a2c95bf0dae7de920012025-08-20T03:38:30ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/281383281383On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach SpacesFarrukh Mukhamedov0Mansoor Saburov1Department of Computational & Theoretical Sciences, Faculty of Sciences, International Islamic University Malaysia, P.O. Box 141, 25710, Kuantan, MalaysiaDepartment of Computational & Theoretical Sciences, Faculty of Sciences, International Islamic University Malaysia, P.O. Box 141, 25710, Kuantan, MalaysiaWe unify all known iterative methods by introducing a new explicit iterative scheme for approximation of common fixed points of finite families of total asymptotically I-nonexpansive mappings. Note that such a scheme contains a particular case of the method introduced by (C. E. Chidume and E. U. Ofoedu, 2009). We construct examples of total asymptotically nonexpansive mappings which are not asymptotically nonexpansive. Note that no such kind of examples were known in the literature. We prove the strong convergence theorems for such iterative process to a common fixed point of the finite family of total asymptotically I-nonexpansive and total asymptotically nonexpansive mappings, defined on a nonempty closed-convex subset of uniformly convex Banach spaces. Moreover, our results extend and unify all known results.http://dx.doi.org/10.1155/2012/281383 |
| spellingShingle | Farrukh Mukhamedov Mansoor Saburov On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces Journal of Applied Mathematics |
| title | On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_full | On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_fullStr | On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_short | On Unification of the Strong Convergence Theorems for a Finite Family of Total Asymptotically Nonexpansive Mappings in Banach Spaces |
| title_sort | on unification of the strong convergence theorems for a finite family of total asymptotically nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/2012/281383 |
| work_keys_str_mv | AT farrukhmukhamedov onunificationofthestrongconvergencetheoremsforafinitefamilyoftotalasymptoticallynonexpansivemappingsinbanachspaces AT mansoorsaburov onunificationofthestrongconvergencetheoremsforafinitefamilyoftotalasymptoticallynonexpansivemappingsinbanachspaces |