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We introduce a new implicit iteration method for finding a solution for a variational inequality involving Lipschitz continuous and strongly monotone mapping over the set of common fixed points for a finite family of nonexpansive mappings on Hilbert spaces.

fixed point theory and applications

An Implicit Iteration Method for Variational Inequalities over the Set of Common Fixed Points for a Finite Family of Nonexpansive Mappings in Hilbert Spaces