Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces
Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T:C→C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzia...
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| Format: | Article |
| Language: | English |
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Wiley
2005-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/IJMMS.2005.1685 |
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| _version_ | 1832562993693458432 |
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| author | Somyot Plubtieng Rabian Wangkeeree |
| author_facet | Somyot Plubtieng Rabian Wangkeeree |
| author_sort | Somyot Plubtieng |
| collection | DOAJ |
| description | Suppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T:C→C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative
scheme converges strongly to some fixed point of T. |
| format | Article |
| id | doaj-art-069dea7ee014462990a9e93cb6bce0c7 |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2005-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-069dea7ee014462990a9e93cb6bce0c72025-02-03T01:21:14ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252005-01-012005111685169210.1155/IJMMS.2005.1685Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spacesSomyot Plubtieng0Rabian Wangkeeree1Department of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandDepartment of Mathematics, Faculty of Science, Naresuan University, Phitsanulok 65000, ThailandSuppose that C is a nonempty closed convex subset of a real uniformly convex Banach space X. Let T:C→C be an asymptotically quasi-nonexpansive mapping. In this paper, we introduce the three-step iterative scheme for such map with error members. Moreover, we prove that if T is uniformly L-Lipschitzian and completely continuous, then the iterative scheme converges strongly to some fixed point of T.http://dx.doi.org/10.1155/IJMMS.2005.1685 |
| spellingShingle | Somyot Plubtieng Rabian Wangkeeree Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces International Journal of Mathematics and Mathematical Sciences |
| title | Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces |
| title_full | Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces |
| title_fullStr | Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces |
| title_full_unstemmed | Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces |
| title_short | Fixed point iteration for asymptotically quasi-nonexpansive mappings in Banach spaces |
| title_sort | fixed point iteration for asymptotically quasi nonexpansive mappings in banach spaces |
| url | http://dx.doi.org/10.1155/IJMMS.2005.1685 |
| work_keys_str_mv | AT somyotplubtieng fixedpointiterationforasymptoticallyquasinonexpansivemappingsinbanachspaces AT rabianwangkeeree fixedpointiterationforasymptoticallyquasinonexpansivemappingsinbanachspaces |