Modified Newton-type processes generating Fejér approximations of regularized solutions to nonlinear equations

We investigate a two-stage algorithm for the construction of a regularizing algorithm that solves approximately a nonlinear irregular operator equation. First, the initial equation is regularized by a shift (Lavrent'ev's scheme). To approximate a solution of the regularized equation, we apply modified Newton and Gauss–Newton type methods, in which the derivative of the operator is calculated at a fixed point for all iterations. Convergence theorems for the processes, error estimates, and the Fejer property of iterations are established.