In this paper, some new iterative schemes for approximating the common element of the set of solutions of an equilibrium problem, the set of fixed points of nonspreading mappings and the set of fixed points of nonexpansive mappings are presented in Hilbert spaces. Some strong convergence theorems are obtained by using some new mathematical ideas and methods. The work that will be done has significance in the area of applied mathematics, economics, optimization theory, engineering sciences and some others.