Viscosity Approximation Methods with Errors and Strong Convergence Theorems for a Common Point of Pseudocontractive and Monotone Mappings: Solutions of Variational Inequality Problems

Abstract

We introduce two proximal iterative algorithms with errors which converge strongly to the common solution of certain variational inequality problems for a finite family of pseudocontractive mappings and a finite family of monotone mappings. The strong convergence theorems are obtained under some mild conditions. Our theorems extend and unify some of the results that have been proposed for this class of nonlinear mappings.Clearly, the class of pseudocontractive mappings includes the class of strict pseudocontractive mappings and the class of nonexpansive mappings. We denote by ( ) the set of fixed points of ; that is, ( ) = { ∈ : = }.