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Weak convergence theorem for new nonexpansive mappings in Banach spaces and its applications. (English) Zbl 1219.47115
Summary: A new nonexpansive mapping in a Banach space which is called generalized nonexpansive was introduced by the authors [J. Approx. Theory 149, No. 1, 1–14 (2007; Zbl 1152.46012)]. In this paper, we prove a weak convergence theorem for finding a fixed point of a generalized nonexpansive mapping in a Banach space. Moreover, using this result, we consider a proximal-type algorithm and the feasibility problem.
MSC:
47J25Iterative procedures (nonlinear operator equations)
47H09Mappings defined by “shrinking” properties
47H07Monotone and positive operators on ordered topological linear spaces
47H10Fixed point theorems for nonlinear operators on topological linear spaces