COMBINED NEWTON-KURCHATOV METHOD UNDER THE GENERALIZED LIPSCHITZ CONDITIONS FOR THE DERIVATIVES AND DIVIDED DIFFERENCES

The local convergence of combined iterative process, built on the basis of Newton's method and Kurchatov's method of linear interpolation, for solving of nonlinear operator equations in Banach space under the generalized Lipschitz conditions for the derivative of the first order and divided differences of the first and second order is proved. The radius of the convergence ball and convergence order of the method are determined, the ball of uniqueness of the solution of nonlinear equation is found.