Convergence of iterative method for problem with free phase in case of isometric operator

The problem with free phase is the problem in which only the modulus of the right hand side is given. The case is considered when a linear operator of the problem is acting in complex Hilbertian spaces. The pseudo-solutions of the problem is found from a nonlinear functional equation. The convergence of an iterative method for this equation is proved for the case, when the operator of the problem is isometric.