Journal
ACTA APPLICANDAE MATHEMATICAE
Volume 110, Issue 3, Pages 1211-1224Publisher
SPRINGER
DOI: 10.1007/s10440-009-9502-9
Keywords
Variational inequality; Iterative method; Nonexpansive mapping; Fixed point
Categories
Funding
- NSC [97-2221-E-230-017]
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In this paper, we introduce a new system of general variational inequalities in Banach spaces. We establish the equivalence between this system of variational inequalities and fixed point problems involving the nonexpansive mapping. This alternative equivalent formulation is used to suggest and analyze a modified extragradient method for solving the system of general variational inequalities. Using the demi-closedness principle for nonexpansive mappings, we prove the strong convergence of the proposed iterative method under some suitable conditions.
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