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Zbl 1124.65056
Ceng, Lu-Chuan; Yao, Jen-Chih
An extragradient-like approximation method for variational inequality problems and fixed point problems. (English)
[J] Appl. Math. Comput. 190, No. 1, 205-215 (2007). ISSN 0096-3003

Summary: The purpose of this paper is to investigate the problem of finding a common element of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. The authors introduce an extragradient-like approximation method based on the so-called extragradient method and a viscosity approximation method. A strong convergence theorem is proved for two iterative sequences generated by this method.

MSC 2000:: *65K10 Optimization techniques (numerical methods)
49J40 Variational methods including variational inequalities
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
49M25 Finite difference methods
47H09 Mappings defined by "shrinking" properties

Keywords: extragradient-like approximation method; variational inequality; fixed point; monotone mapping; nonexpansive mapping; strong convergence

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