Viscosity approximation method for a variational problem.

By combining the works of Moudafi [A. Moudafi, J. Math. Anal. Appl., 241 (2000), 46-55] and Iiduka and Takahashi [H. Iiduka, W. Takahashi, Nonlinear Anal., 61 (2005), 341-350], we introduce an iterative process that converges strongly to a particular solution of a variational inequality problem. We also study the stability of the algorithm under relatively small perturbation and we apply the obtained results to the study of a constrained optimization problem and a problem of common fixed points of two nonexpansive mappings. Some numerical experiments are provided to study the affect of some parameters on the speed of the convergence of the considered algorithm. [ABSTRACT FROM AUTHOR]