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A viscosity approximation scheme for system of equilibrium problems, nonexpansive mappings and monotone mappings. (English) Zbl 1178.47047
Summary: We introduce a new viscosity approximation scheme based on the extragradient method for finding a common element of the set of solutions to a system of equilibrium problems, the set of fixed points of an infinite family of nonexpansive mappings and the set of solutions to the variational inequality for a monotone, Lipschitz continuous mapping. Several convergence results for the sequences generated by these processes in Hilbert spaces are derived.
MSC:
47J25Iterative procedures (nonlinear operator equations)
49J40Variational methods including variational inequalities
47H09Mappings defined by “shrinking” properties
47H05Monotone operators (with respect to duality) and generalizations