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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| Main Author: | |
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| Format: | Article |
| Language: | English |
| Published: |
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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| Summary: | 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. |
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| ISSN: | 0161-1712 1687-0425 |