We are concerned with finding a common solution to an equilibrium problem associated with a bifunction, and a constrained convex minimization problem. We propose an iterative fixed point algorithm and prove that the algorithm generates a sequence strongly convergent to a common solution. The common solution is identified as the unique solution of a certain variational inequality.

Keywords: Nonexpansive mapping, equilibrium problem, fixed point, convex minimization, averaged mapping, iterative method, variational inequality