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Strong and $\Delta$ convergence theorems for multivalued mappings in CAT(0) spaces. (English) Zbl 1176.47056
Summary: We show strong and $\Delta$ convergence for Mann iterations of a multivalued nonexpansive mapping whose domain is a nonempty closed convex subset of a CAT(0) space. The results we obtain are analogs of Banach space results by {\it Y.--S.\thinspace Song} and {\it H.--J.\thinspace Wang} [Nonlinear Anal., Theory Methods Appl. 70, No. 4 (A), 1547--1556 (2009; Zbl 1175.47063); Comput. Math. Appl. 55, No. 12, 2999--3002 (2008; Zbl 1142.47344)]. Strong convergence of Ishikawa iterations is also included.

47J25Iterative procedures (nonlinear operator equations)
47H04Set-valued operators
47H09Mappings defined by “shrinking” properties
Full Text: DOI EuDML