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Zbl 1191.47077
Dhompongsa, S.; Fupinwong, W.; Kaewkhao, A.
Common fixed points of a nonexpansive semigroup and a convergence theorem for Mann iterations in geodesic metric spaces. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 70, No. 12, A, 4268-4273 (2009). ISSN 0362-546X

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.
[Ioan I. Vrabie (Iaşi)]

MSC 2000:: *47H20 Semigroups of nonlinear operators
54H25 Fixed-point theorems in topological spaces
47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties

Keywords: geodesic metric space; nonexpansive semigroup; fixed point

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