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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 involving nonlinear operators
47H10 Fixed-point theorems
47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H05 Monotone operators and generalizations
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References:

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