Iterative Newton-type methods with projecting for solution of nonlinear ill-posed operator equations

We propose and study a class of iterative methods of the Newton type for approximate solution of nonlinear ill-posed operator equations without the regularity property. A possible a priori information concerning the unknown solution is treated by the projecting onto a closed convex subset containing the solution. The two ways of arranging of the computational process are considered. The first one requires the stopping of iterations at an appropriate step, while the second ensures obtaining of an iterative sequence which stabilizes within a small neighborhood of the solution.