In this paper, we introduce two iterative schemes by the general iterative method for finding a fixed point of a nonexpansive mapping in Hilbert spaces. Then we prove a strong convergence theorem of Ces�ro mean iterations to solve a unique solution of the variational inequality which is the optimization problem. This result extends and improves the corresponding results of Plubtieng and Punpaeng [9], Shioji and Takahashi [10], and many others.

equilibrium problem, viscosity approximation method, nonexpansive mapping, variational inequalities, fixed point.