On the approximation of solutions to nonlinear operators between metric spaces

A Gauss-Seidel type method for the solution of linear systems, based on the decomposition of the system matrix into four matrices blocks, has been proposed by R. Varga in |3|. The convergence of this method was studied in [1] and [2].

In this paper we shall extend the ideas contained in the above quoted works to the case of nonlinear systems equations.