George, S.Elmahdy, A.I.2026-02-052010International Journal of Mathematical Analysis, 2010, 4, 45-48, pp. 2211-222813128876https://idr.nitk.ac.in/handle/123456789/27376An iteratively regularized projection method, which converges quadratically, has been considered for obtaining stable approximate solution to nonlinear ill-posed operator equations F(x) = y where F : D(F) ? X ? X is a nonlinear monotone operator defined on the real Hilbert space X: We assume that only a noisy data y? with y-y? ? ? are available. Under the assumption that the Fréchet derivative F? of F is Lipschitz continuous, a choice of the regularization parameter using an adaptive selection of the parameter and a stopping rule for the iteration index using a majorizing sequence are presented. We prove that under a general source condition on x<inf>0</inf> - x?, the error between the regularized approximation where P<inf>h</inf> is an orthog-onal projection on to a nite dimensional subspace X<inf>h</inf> of X) and the solution x? is of optimal order.Majorizing sequenceMonotone operatorNonlinear Ill-posed operatorQuadratic convergenceRegularized projection method