Strong convergence of a self-adaptive method for the split feasibility problem

Self-adaptive methods which permit step-sizes being selected self-adaptively are effective methods for solving some important problems, e. g., variational inequality problems. We devote this paper to developing and improving the self-adaptive methods for solving the split feasibility problem. A new improved self-adaptive method is introduced for solving the split feasibility problem. As a special case, the minimum norm solution of the split feasibility problem can be approached iteratively.