WEAK AND NORM CONVERGENCE OF A PARALLEL PROJECTION METHOD IN HILBERT-SPACES

We show that for a parallel projection method for finding the common p oint of convex sets in a Hilbert space, under very mild conditions abo ut the variable weights and the variable relaxation parameters, the co nstructed sequence is weakly convergent to a point of the intersection of the sets. we also prove norm convergence of the sequence under add itional conditions on the convex sets.