Argyros, I.K.George, S.Padikkal, P.2026-02-052017Nonlinear Studies, 2017, 24, 2, pp. 257-27113598678https://idr.nitk.ac.in/handle/123456789/25780In this paper we report on a method for regularizing a nonlinear ill-posed operator equation in Hilbert scales. The proposed method is a combination of Lavrentiev regularization method and a Modified Newton's method in Hilbert scales . Under the assumptions that the operator F is continu- ously differentiable with a Lipschitz-continuous first derivative and that the solution of (1.1) fulfils a general source condition, we give an optimal order convergence rate result with respect to the general source function. © CSP - Cambridge, UK; I & S - Florida, USA, 2017.Adaptive choiceHilbert scalesIterative regularizationNonlinear ill-posed equations