A WEAK CONVERGENCE THEOREM FOR SOLVING THE SPLIT COMMON FIXED POINT PROBLEM IN TWO BANACH SPACES AND APPLICATIONS

In this paper, we consider the split common fixed point problem in two Banach spaces. Using the idea of Mann's iteration, we prove a weak convergence theorem for finding a solution of the split common fixed point problem in two Banach spaces. It seems that such a theorem of Mann's type iteration is first outside Hilbert spaces. We apply this theorem to get well-known and new weak convergence theorems which are connected with the feasibility problem, the split common null point problem and the split common fixed point problem in Hilbert spaces and in Banach spaces.