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Zbl 1162.65030
Yao, Yonghong; Liou, Yeong-Cheng; Kang, Shin Min
Strong convergence of an iterative algorithm on an infinite countable family of nonexpansive mappings.
(English)
[J] Appl. Math. Comput. 208, No. 1, 211-218 (2009). ISSN 0096-3003

The following iterative procedure is studied $$x_{n+1}=\alpha_{n}f(x_{n})+\beta_{n}x_{n}+(1-\alpha_{n}-\beta_{n})W_{n}x_{n}$$ where $x_{0}$ is arbitrary. The authors prove that if $f$ is contractive and some other conditions are fulfilled the sequence $x_{n}$ converges strongly to the solution of a variational inequality.
[Erwin Schechter (Moers)]
MSC 2000:
*65J15 Equations with nonlinear operators (numerical methods)
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

Keywords: strong convergence; iterative algorithm; infinite countable family of nonexpansive mappings; common fixed point; variational inequality

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