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On relaxed viscosity iterative methods for variational inequalities in Banach spaces. (English) Zbl 1178.65074
Summary: The authors propose and analyze a relaxed viscosity iterative method for a commutative family of nonexpansive self-mappings defined on a nonempty closed convex subset of a reflexive Banach space. They prove that the sequence of approximate solutions generated by the proposed iterative algorithm converges strongly to a solution of a variational inequality. This relaxed viscosity iterative method is an extension and variant form of the original viscosity iterative method. The results of this paper can be viewed as an improvement and generalization of the previously known techniques appeared in the literature.
MSC:
65K15Numerical methods for variational inequalities and related problems
49J40Variational methods including variational inequalities
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47J20Inequalities involving nonlinear operators
47J30Variational methods (nonlinear operator equations)