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Common fixed points of a nonexpansive semigroup and a convergence theorem for Mann iterations in geodesic metric spaces. (English) Zbl 1191.47077
The authors prove a convergence theorem for the sequence of Mann iterations, for a strongly continuous semigroup of nonexpansive mappings acting on a closed convex subset of a complete CAT(0) space, to a common fixed point of all mappings in the semigroup. They also prove a result concerning the limits of subsequences of Mann iterations of multivalued nonexpansive mappings on metric spaces of hyperbolic type.

MSC:
47H20 Semigroups of nonlinear operators
54H25 Fixed-point and coincidence theorems (topological aspects)
47J25 Iterative procedures involving nonlinear operators
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
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