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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.

47H20Semigroups of nonlinear operators
54H25Fixed-point and coincidence theorems in topological spaces
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
Full Text: DOI
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