In this paper we deal with the von Neumann alternating projection method xk+1 = PAPBxk and with its generalization of the form xk+1 = PA(xk + k(PAPBxk xk)), where A;B are closed and convex subsets of a Hilbert space H and FixPAPB 6= ?. We do not suppose that A \ B 6= ?. We give su¢ cient conditions for the weak convergence of the sequence (xk) to FixPAPB in the general case and in the case A is...
