Parallel synchronous algorithm for nonlinear fixed point problems

with respect to the Euclidian norm, where F :Rn →Rn is a nonlinear operator. Section 2 is devoted to a brief description of asynchronous parallel algorithm. In Section 3, we prove the main result concerning the convergence of the general algorithm in the synchronous case to a fixed point of a nonlinear operator fromRn to Rn. A particular case of this algorithm (algorithm of Jacobi) is applied in Section 4 to the operator F = (I +T)−1 which is called the proximal mapping associated with the maximal monotone operator T (see Rockafellar [10]).