Strong convergence of viscosity approximation methods for the fixed-point of pseudo-contractive and monotone mappings

In this paper, we introduce a viscosity iterative process, which converges strongly to a common element of the set of fixed points of a pseudo-contractive mapping and the set of solutions of a monotone mapping. We also prove that the common element is the unique solution of certain variational inequality. The strong convergence theorems are obtained under some mild conditions. The results presented in this paper extend and unify most of the results that have been proposed for this class of nonlinear mappings.