Convergence of the consecutive approximation method of a solution of the nonlinear problems of the antennas synthesis

The weak convergence of a consecutive approximation method of a solution of the nonlinear equation is proved. The problem of searching of a pseudo-solution of the equations with a free phase is reduced to this equation. The operator of the equation is a superposition of the linear limited operator and nonlinear operator (modulus of a complex function). In this case the linear operator of the problem is completely continuous.