Strong Convergence Theorem for an Equilibrium Problem and a Nonexpansive Semigroup in Hilbert Spaces

In this paper, we introduce a new iterative method for finding a common element of the set of solutions of an equilibrium problem and the set of all common fixed points of a nonexpansive semigroup, and prove the strong convergence theorem in Hilbert spaces. This method is based on the proximal point method applying to equilibrium problem combining with a Mann iterative scheme by the viscosity approximation method to find a common fixed points of a nonexpansive semigroup.