Vasin, V.George, S.2026-02-052014Journal of Inverse and Ill-Posed Problems, 2014, 22, 4, pp. 593-6079280219https://doi.org/10.1515/jip-2013-0025https://idr.nitk.ac.in/handle/123456789/26483Recently, Vasin [J. Inverse Ill-Posed Probl. 21 (2013), 109-123] considered a new iterative method for approximately solving nonlinear ill-posed operator equation in Hilbert spaces. In this paper we introduce a modified form of the method considered by Vasin. This paper weakens the conditions needed in the existing results. We use a center-type Lipschitz condition in our convergence analysis instead of a Lipschitz-type condition used in [J. Inverse Ill-Posed Probl. 21 (2013), 109-123]. This way a tighter convergence analysis is obtained and under less computational cost, since the more precise and easier to compute center-Lipschitz instead of the Lipschitz constant is used in the convergence analysis. Order optimal error bounds are given in case the regularization parameter is chosen a priori and by the adaptive method of Pereverzev and Schock [SIAM J. Numer. Anal. 43 (2005), 2060-2076]. A numerical example of a nonlinear integral equation proves the efficiency of the proposed method. © 2014 by De Gruyter.Error analysisIntegral equationsInverse problemsMathematical operatorsNewton-Raphson methodNonlinear equationsParameterizationConvergence analysisIll-posed equationsIll-posed operator equationIterative approximationsLipschitz conditionsNonlinear integral equationsRegularization parametersTikhonov methodNumerical methods