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Zbl 1178.47047
Peng, Jian-Wen; Yao, Jen-Chih
A viscosity approximation scheme for system of equilibrium problems, nonexpansive mappings and monotone mappings. (English)
[J] Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71, No. 12, A, 6001-6010 (2009). ISSN 0362-546X

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 2000:: *47J25 Methods for solving nonlinear operator equations (general)
49J40 Variational methods including variational inequalities
47H09 Mappings defined by "shrinking" properties
47H05 Monotone operators (with respect to duality)

Keywords: system of equilibrium problems; extragradient methods; nonexpansive mapping; monotone mapping; viscosity approximation scheme; strong convergence

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