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Approximating common fixed points of countable families of strongly nonexpansive mappings. (English) Zbl 1147.47050
The authors study the problem of approximating common fixed points of a countable infinite family of strongly nonexpansive mappings in Banach spaces. Applications to the convex feasibility problem and a proximal-type algorithm are also given.

##### MSC:
 47J25 Iterative procedures involving nonlinear operators 47H10 Fixed-point theorems 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 90C48 Programming in abstract spaces