A viscosity approximation scheme for system of equilibrium problems, nonexpansive mappings and monotone mappings

Abstract In this paper, 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 were derived.

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