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

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.