Weak and Strong Convergence of Two Algorithms for the Split Fixed Point Problem

Abstract

Two iterative algorithms are proposed for the split fixed point problem. The first algorithm is shown to be weakly convergent and the second one to be strongly convergent. One feature of these algorithms is that the step sizes are chosen in such a way that no priori knowledge of the operator norms is required. A new idea is introduced in order to prove strong convergence of the second algorithm.