Approximation of common fixed points of a countable family of nonexpansive mappings in a Banach space. (English) Zbl 1130.47045

Aoyama, Koji; Kimura, Yasunori; Takahashi, Wataru; Toyoda, Masashi

Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 67, No. 8, 2350-2360 (2007).

The authors use a Halpern-type iteration to approximate a common fixed point of a countable family of nonexpansive mappings with some additional conditions in a uniformly convex Banach space whose norm is uniformly Gâteaux differentiable. They also apply the result to the problem of finding a zero of an accretive operator.

Reviewer: Satit Saejung (Khon Kaen)

MSC:

47J25	Iterative procedures involving nonlinear operators
47H10	Fixed-point theorems
47H09	Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
41A65	Abstract approximation theory (approximation in normed linear spaces and other abstract spaces)
47H06	Nonlinear accretive operators, dissipative operators, etc.

Keywords:

fixed point; nonexpansive mapping; Halpern iteration; accretive operator

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