Iterative methods for strict pseudo-contractions in Hilbert spaces

Abstract

Let { T i } i = 1 N be N strict pseudo-contractions defined on a closed convex subset C of a real Hilbert space H . Consider the problem of finding a common fixed point of these mappings and consider the parallel and cyclic algorithms for solving this problem. We will prove the weak convergence of these algorithms. Moreover, by applying additional projections, we further prove that these algorithms can be modified to have strong convergence.