Convergence of the two-step combined method and uniqueness of the solution of nonlinear operator equations

Local convergence of the two-step differential-difference method for solving nonlinear operator equations for generalized Lipschitz conditions for Fréchet derivatives of the first and second order and divided differences of the first order has been proven. There have been found estimations of the convergence ball’s radii of this method and the uniqueness ball of solution of nonlinear equations. There has been established the superquadratical order of the convergence of the two-step combined method and a comparison of the results with the known ones has been made.