On the fixed points of affine nonexpansive mappings
Let K be a closed convex bounded subset of a Banach space X and let T:K→K be a continuous affine mapping. In this note, we show that (a) if T is nonexpansive then it has a fixed point, (b) if T has only one fixed point then the mapping A=(I+T)/2 is a focusing mapping; and (c) a continuous mapping S:...
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| Format: | Article |
| Language: | English |
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Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S016117120100638X |
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| _version_ | 1832562574254669824 |
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| author | Hülya Duru |
| author_facet | Hülya Duru |
| author_sort | Hülya Duru |
| collection | DOAJ |
| description | Let K be a closed convex bounded subset of a Banach space X and let T:K→K be a continuous affine mapping. In this note, we show that (a) if T is nonexpansive then it has a fixed point, (b) if T has only one fixed point then the mapping A=(I+T)/2 is a focusing mapping; and (c) a continuous mapping S:K→K has a fixed point if and only if, for each x∈k, ‖(An∘S)(x)−(S∘An)(x)‖→0for some strictly nonexpansive affine mapping T. |
| format | Article |
| id | doaj-art-ec0c2c0da26f4890bfd2e97af4449bbc |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-ec0c2c0da26f4890bfd2e97af4449bbc2025-02-03T01:22:24ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01281168568810.1155/S016117120100638XOn the fixed points of affine nonexpansive mappingsHülya Duru0Department of Mathematics, Faculty of Sciences, Istanbul University, Vezneciler, Istanbul 34459, TurkeyLet K be a closed convex bounded subset of a Banach space X and let T:K→K be a continuous affine mapping. In this note, we show that (a) if T is nonexpansive then it has a fixed point, (b) if T has only one fixed point then the mapping A=(I+T)/2 is a focusing mapping; and (c) a continuous mapping S:K→K has a fixed point if and only if, for each x∈k, ‖(An∘S)(x)−(S∘An)(x)‖→0for some strictly nonexpansive affine mapping T.http://dx.doi.org/10.1155/S016117120100638X |
| spellingShingle | Hülya Duru On the fixed points of affine nonexpansive mappings International Journal of Mathematics and Mathematical Sciences |
| title | On the fixed points of affine nonexpansive mappings |
| title_full | On the fixed points of affine nonexpansive mappings |
| title_fullStr | On the fixed points of affine nonexpansive mappings |
| title_full_unstemmed | On the fixed points of affine nonexpansive mappings |
| title_short | On the fixed points of affine nonexpansive mappings |
| title_sort | on the fixed points of affine nonexpansive mappings |
| url | http://dx.doi.org/10.1155/S016117120100638X |
| work_keys_str_mv | AT hulyaduru onthefixedpointsofaffinenonexpansivemappings |