Iterations of parallel convex projections in hilbert spaces

The problem of finding a common point of closed and convex sets in a Hilbert space is considered. A general iterative method of parallel projections is presented, in which the current iterate is projected simultaneously onto selected sets and the new iterate is a relaxed convex combination of the projections. Weak and strong convergence results are established and the influence of the relaxation coefficients is discussed. Convergence to a least-squares solution when the sets do not intersect is also proved.