Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces
In this paper, we prove a fixed point theorem for the selfmaps of a closed convex and bounded subset of the Banach space satisfying a generalized nonexpansive type condition. Some results concerning the approximations of fixed points with Krasnoselskii and Mann type iterations are also proved under...
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| Format: | Article |
| Language: | English |
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Etamaths Publishing
2014-10-01
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| Series: | International Journal of Analysis and Applications |
| Online Access: | http://etamaths.com/index.php/ijaa/article/view/390 |
| _version_ | 1831569899341742080 |
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| author | Bapurao C. Dhage |
| author_facet | Bapurao C. Dhage |
| author_sort | Bapurao C. Dhage |
| collection | DOAJ |
| description | In this paper, we prove a fixed point theorem for the selfmaps of a closed convex and bounded subset of the Banach space satisfying a generalized nonexpansive type condition. Some results concerning the approximations of fixed points with Krasnoselskii and Mann type iterations are also proved under suitable conditions. Our results include the well-known result of Kannan (1968) and Bose and Mukherjee (1981) as the special cases with a different and constructive method. |
| first_indexed | 2024-12-17T12:41:19Z |
| format | Article |
| id | doaj.art-76cc04285ec3454c853b9f5750e05846 |
| institution | Directory Open Access Journal |
| issn | 2291-8639 |
| language | English |
| last_indexed | 2024-12-17T12:41:19Z |
| publishDate | 2014-10-01 |
| publisher | Etamaths Publishing |
| record_format | Article |
| series | International Journal of Analysis and Applications |
| spelling | doaj.art-76cc04285ec3454c853b9f5750e058462022-12-21T21:47:58ZengEtamaths PublishingInternational Journal of Analysis and Applications2291-86392014-10-016214415399Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach SpacesBapurao C. Dhage0kasubai, Gurukul Colony, Ahmedpur-413 515, Dist. Latur, Maharashtra, IndiaIn this paper, we prove a fixed point theorem for the selfmaps of a closed convex and bounded subset of the Banach space satisfying a generalized nonexpansive type condition. Some results concerning the approximations of fixed points with Krasnoselskii and Mann type iterations are also proved under suitable conditions. Our results include the well-known result of Kannan (1968) and Bose and Mukherjee (1981) as the special cases with a different and constructive method.http://etamaths.com/index.php/ijaa/article/view/390 |
| spellingShingle | Bapurao C. Dhage Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces International Journal of Analysis and Applications |
| title | Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces |
| title_full | Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces |
| title_fullStr | Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces |
| title_full_unstemmed | Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces |
| title_short | Approximating Fixed Points of Generalized Nonexpansive Mappings in Banach Spaces |
| title_sort | approximating fixed points of generalized nonexpansive mappings in banach spaces |
| url | http://etamaths.com/index.php/ijaa/article/view/390 |
| work_keys_str_mv | AT bapuraocdhage approximatingfixedpointsofgeneralizednonexpansivemappingsinbanachspaces |