Two-step methods and relaxed two-step methods for solving the split equality problem

The inverse problems as a classical mathematical model arise frequently in practical applications. While the split equality problem is an inverse problem arising frequently in signal processing, phase retrieval and medical image reconstruction etc. which is also an important extension of the split feasibility problem. In this paper, motivated and inspired by an idea for solving a variational inequality, we proved that several two-step methods and relaxed two-step methods can be applied to solve the split equality problem. What’s more, we proved that the technique of optimal step size for solving the variational inequality is still efficient for the split equality problem. Meanwhile, we also confirmed that these provided methods also apply to solving the split feasibility problem.