An iterative method for nonexpansive semigroups, variational inclusions and generalized equilibrium problems

The purpose of this paper is to prove strong convergence theorems for finding a common element of the set of common fixed points of a one-parameter nonexpansive semigroup, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. Using our results, we obtain the mean ergodic theorem for nonexpansive mappings in Hilbert spaces. Our results extend many recent important results.