Composite Algorithms for Minimization over the Solutions of Equilibrium Problems and Fixed Point Problems

The purpose of this paper is to solve the minimization problem of finding x∗ such that x∗=argminx∈Γ‖x‖2, where Γ stands for the intersection set of the solution set of the equilibrium problem and the fixed points set of a nonexpansive mapping. We first present two new composite algorithms (one implicit and one explicit). Further, we prove that the proposed composite algorithms converge strongly to x∗