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We introduce a general iterative method for finding the solution of the variational inequality problem over the fixed point set of a nonexpansive semigroup in a Hilbert space. We prove that the sequence converges strongly to a common element of the above two sets under some parameters controlling conditions. Our results improve and generalize many known corresponding results.

General Iterative Algorithm for Nonexpansive Semigroups and Variational Inequalities in Hilbert Spaces