In this paper, we propose two iteration algorithms for finding a common element of the solution set of equilibrium problems and the set of fixed points of a nonexpansive mapping in a real Hilbert space. Based on the assumption on the pseudomonotonicity of the bifunction associated with the equilibrium problems, the weak convergence of  the schemes is established. As an application, a problem of finding a common element of the set of solutions of variational inequalities and the set of fixed points of a nonexpansive mapping is solved.

equilibrium problems, nonexpansive, pseudomonotone, linesearch, fixed point.