On the fixed points of affine nonexpansive mappings

Hülya Duru

International Journal of Mathematics and Mathematical Sciences, 2001, vol. 28, 1-4

Abstract:

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 , ‖ ( A n ∘ S ) ( x ) − ( S ∘ A n ) ( x ) ‖ → 0 for some strictly nonexpansive affine mapping T .

Date: 2001
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:253620

DOI: 10.1155/S016117120100638X

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