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Approximating fixed points of nonexpansive mappings in a Banach space by metric projections. (English) Zbl 1190.47072
Summary: A strong convergence theorem for nonexpansive mappings in a uniformly convex and smooth Banach space is proved by using metric projections. This theorem is different from the recent strong convergence theorem due to {\it H.-K.\thinspace Xu} [Bull. Aust. Math. Soc. 74, No. 1, 143--151 (2006; Zbl 1126.47056)] which was established by generalized projections.

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