An analog of the method of continuation of solution with respect to the parameter for nonlinear operator equations

A process of second order is constructed for the solution of nonlinear operator equations which is an analog of the method of continuation of solution with respect to the parameter. For each value of the parameter the Newton–Kantorovich iteration formula is applied only once in all. The quadratic convergence of the process is ensured by the specification of the parameter by a special formula. The process under consideration enables us to avoid the singular points of the derivative of the nonlinear operator on the left-hand side of the operator equation.