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Strong convergence of approximated sequences for nonexpansive mappings in Banach spaces. (English) Zbl 0888.47034
Summary: We study the convergence of the sequence defined by $x_0\in C,\qquad x_{n+1} = \alpha_{n}x + (1-\alpha_{n})Tx_n,\qquad n=0,1,2, \ldots,$ where $$0 \leq \alpha_n \leq 1$$ and $$T$$ is a nonexpansive mapping from a closed convex subset of a Banach space into itself.

##### MSC:
 47H09 Contraction-type mappings, nonexpansive mappings, $$A$$-proper mappings, etc. 47J25 Iterative procedures involving nonlinear operators 49M05 Numerical methods based on necessary conditions
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##### References:
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