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A note on Picard iterates of nonexpansive mappings

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Kim E., Kirk W.

Annales Polonici Mathematici

2001

tom 76

nr 3

189-196

Let X be a Banach space, C a closed subset of X, and T:C → C a nonexpansive mapping. It has recently been shown that if X is reflexive and locally uniformly convex and if the fixed point set F(T) of T has nonempty interior then the Picard iterates of the mapping T always converge to a point of F(T). In this paper it is shown that if T is assumed to be asymptotically regular, this condition can be weakened much further. Finally, some observations are made about the geometric conditions imposed.

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1 Annales Polonici Mathematici

1 Kim E.

1 Kirk W.

1 2001

Wyniki wyszukiwania

A note on Picard iterates of nonexpansive mappings