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Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces. (English) Zbl 1111.47057
By using viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces, the author obtains sufficient and necessary conditions for the iterative sequence $x_{n+1} = \alpha _{n+1}f(x_{n}) + (1 - \alpha _{n+1})T_{n+1}x_{n}$ to converge strongly to a common fixed point of the family. His statements extend and improve some recent results.

MSC:
 47J25 Iterative procedures (nonlinear operator equations) 47H10 Fixed-point theorems for nonlinear operators on topological linear spaces 47H09 Mappings defined by “shrinking” properties 47H05 Monotone operators (with respect to duality) and generalizations
Full Text:
References:
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