A MODIFIED RELAXED CQ ALGORITHM FOR THE SOLUTION OF MULTIPLE SPLIT FEASIBILITY PROBLEM IN REAL HILBERT SPACES

Abstract

Let  be Hilbert spaces, let   be closed convex nonempty subsets of  and  respectively and let  be bounded linear operators. The problem of finding  such that  is called the multiple split feasibility problem (MSFP). We introduced the multiple split feasibility problem (MSFP) as a natural generalization of the classical split feasibility problem and modify the relaxed CQ algorithm for solution of the split feasibility problem (SFP) for the iterative solution of the MSFP. We establish the weak convergence of this modified algorithm under very mild conditions on the iterative parameters. Using an Ishikawa like process, strong convergence is established.