Strong convergence theorem for a generalized equilibrium problem and a nonexpansive mapping in a Hilbert space Original Research Article

We introduce an iterative method for finding a common element of the set of solutions of a generalized equilibrium problem and the set of fixed points of a nonexpansive mapping in a Hilbert space and then obtain that the sequence converges strongly to a common element of two sets. Using this result, we prove three new strong convergence theorems in fixed point problems, variational inequalities and equilibrium problems.