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Zbl 1111.47057
Chang, Shih-Sen
Viscosity approximation methods for a finite family of nonexpansive mappings in Banach spaces.
(English)
[J] J. Math. Anal. Appl. 323, No. 2, 1402-1416 (2006). ISSN 0022-247X

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.
[Edward Prempeh (Kumasi)]
MSC 2000:
*47J25 Methods for solving nonlinear operator equations (general)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
47H09 Mappings defined by "shrinking" properties
47H05 Monotone operators (with respect to duality)

Keywords: finite family of nonexpansive maps; common fixed points; viscosity approximation method; strong convergence; uniformly smooth Banach space

Cited in: Zbl 1212.47086 Zbl 1140.47057

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