Strong convergence algorithm for proximal split feasibility problem

The purpose of this paper is to propose an algorithm for solving the proximal split feasibility problems and fixed point problems in Hilbert spaces. The algorithm is motivated by the inertial method and the split proximal algorithm with a self-adaptive stepsize such that their implementation does not need any prior information about the operator norm. We also apply our main result to the split variational inclusion problem and split equilibrium problem. Further, a numerical example is given to study the efficiency and implementation of our scheme.