Erappa, M.E.George, S.Kunhanandan, M.2026-02-052014Journal of Integral Equations and Applications, 2014, 26, 1, pp. 91-1168973962https://doi.org/10.1216/JIE-2014-26-1-91https://idr.nitk.ac.in/handle/123456789/26640In this paper regularized solutions of ill-posed Hammerstein type operator equation KF(x) = y, where K : X ? Y is a bounded linear operator with non-closed range and F : X ? X is non-linear, are obtained by a two step Newton type iterative method in Hilbert scales, where the available data is y? in place of actual data y withy-y?? ?. We require only a weaker assumptionF'(x<inf>0</inf>)x?x<inf>-b</inf> compared to the usual assumptionF'(x?)x?x<inf>-b</inf>, where x? is the actual solution of the problem, which is assumed to exist, and x<inf>0</inf> is the initial approximation. Two cases, viz-aviz, (i) when F'(x<inf>0</inf>) is boundedly invertible and (ii) F'(x<inf>0</inf>) is non-invertible but F is monotone operator, are considered. We derive error bounds under certain general source conditions by choosing the regularization parameter by an a priori manner as well as by using a modified form of the adaptive scheme proposed by Perverzev and Schock . © 2014 Rocky Mountain Mathematics Consortium.Adaptive choiceHilbert scalesIll-posed problemsNewton's methodTikhonov regularization