Iterative regularization methods for ill-posed Hammerstein-type operator equations in Hilbert scales

In this paper we report on a method for regularizing a nonlinear Hammerstein type operator equation in Hilbert scales. The proposed method is a combination of Lavrentieve regularization method and a Modified Newton's method in Hilbert scales. Under the assumptions that the operator F is continuously differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfills a general source condition, we give an optimal order convergence rate result with respect to the general source function.