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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 Y.–S. Song and H.–J. 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.
MSC:
 47J25 Iterative procedures (nonlinear operator equations) 47H04 Set-valued operators 47H09 Mappings defined by “shrinking” properties
References:
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