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Zbl 1147.49007
Ceng, Lu-Chuan; Wang, Chang-yu; Yao, Jen-Chih
Strong convergence theorems by a relaxed extragradient method for a general system of variational inequalities. (English)
[J] Math. Methods Oper. Res. 67, No. 3, 375-390 (2008). ISSN 1432-2994; ISSN 1432-5217/e

Summary: In this paper, we introduce and study a relaxed extragradient method for finding solutions of a general system of variational inequalities with inverse-strongly monotone mappings in a real Hilbert space. First, this system of variational inequalities is proven to be equivalent to a fixed point problem of nonexpansive mapping. Second, by using the demi-closedness principle for nonexpansive mappings, we prove that under quite mild conditions the iterative sequence defined by the relaxed extragradient method converges strongly to a solution of this system of variational inequalities. In addition, utilizing this result, we provide some applications of the considered problem not just giving a pure extension of existing mathematical problems.

MSC 2000:: *49J40 Variational methods including variational inequalities
47H05 Monotone operators (with respect to duality)
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces

Keywords: nonexpansive mapping; common fixed point; demi-closedness principle; inverse-strongly monotone mapping; general system of variational inequalities

Cited in: Zbl 1235.49019 Zbl 1216.49010 Zbl 1205.65189 Zbl 1203.47064 Zbl 1219.49009 Zbl 1175.49009

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