On the relaxed projection method for the SFPMOS

. This paper presents our investigation into the split feasibility problem with multiple output sets (SF-PMOS), under the assumption that the corresponding convex subsets are level subsets of convex functionals. To approximate the solutions of this problem, we propose a method that combines relaxed projection with a recently proposed technique. Our approach involves establishing a weak convergence theorem for the fixed stepsize, followed by constructing a variable stepsize that is independent of the norm of the linear operator involved. We also modify these methods to ensure strong convergence. As an application, we develop a new relaxed projection algorithm for solving the split feasibility problem.