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

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.
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