An iterative method for fixed point problems, variational inclusions and generalized equilibrium problems

In this paper, we introduce a new iterative scheme for finding a common element of the set of fixed points of a nonexpansive mapping, the set of solutions to a variational inclusion and the set of solutions to a generalized equilibrium problem in a real Hilbert space. Furthermore, using our new iterative scheme, we prove strong convergence theorems which extend many recent important results. Finally, we apply our results to solve an optimization problem in a real Hilbert space.