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Convergence of iterative algorithms for multivalued mappings in Banach spaces. (English) Zbl 1175.47063
Summary: We show strong and weak convergence for Mann iteration of multivalued nonexpansive mappings $T$ in a Banach space. Furthermore, we give a strong convergence of the modified Mann iteration which is independent of the convergence of the implicit anchor-like continuous path $z_t \in tu+(1 - t)Tz_t$.

MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H04Set-valued operators
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
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References:
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