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Zbl 1130.90055
Nadezhkina, N.; Takahashi, W.
Weak convergence theorem by an extragradient method for nonexpansive mappings and monotone mappings. (English)
[J] J. Optim. Theory Appl. 128, No. 1, 191-201 (2006). ISSN 0022-3239; ISSN 1573-2878/e

Summary: In this paper, we introduce an iterative process for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the variational inequality problem for a monotone, Lipschitz-continuous mapping. The iterative process is based on the so-called extragradient method. We obtain a weak convergence theorem for two sequences generated by this process

MSC 2000:: *90C52 Methods of reduced gradient type
49J40 Variational methods including variational inequalities

Keywords: Extragradient method; fixed points; monotone mappings; nonexpansive mappings; variational inequalities

Cited in: Zbl pre06139430 Zbl 1252.65102 Zbl 1223.47080 Zbl 1180.47043 Zbl 1196.47047

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