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Zbl 1223.47109
Zhang, Lijuan; Chen, Junmin; Hou, Zhibin
(Zhang, Li-juan; Chen, Jun-min; Hou, Zhi-bin)
Viscosity approximation methods for nonexpansive mappings and generalized variational inequalities. (Chinese. English summary)
[J] Acta Math. Sin., Chin. Ser. 53, No. 4, 691-698 (2010). ISSN 0583-1431

Summary: Viscosity approximation methods for nonexpansive mappings are studied. Consider the general iteration process $\{x_n\}$, where $x_0\in C$ is arbitrary and $g(x_{n+1})=\alpha_nf(x_n)+(1-\alpha_n)SP_C(g(x_n)-\lambda_n Ax_n)$, $S$ is a nonexpansive self-mapping of a closed convex subset $C$ of a Hilbert space $H$. It is shown that $\{x_n\}$ converges strongly to a common element of the set of fixed points of nonexpansive mapping and the set of solutions of the Noor variational inequality for an inverse strongly monotone mapping which solves some variational inequalities.

MSC 2000:: *47J25 Methods for solving nonlinear operator equations (general)
47H09 Mappings defined by "shrinking" properties
47J20 Inequalities involving nonlinear operators
49J40 Variational methods including variational inequalities

Keywords: viscosity approximation; nonexpansive mapping; variational inequalities; strong convergence

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