Extended Newton-type iteration for nonlinear ill-posed equations in Banach space

Abstract

In this paper, we study nonlinear ill-posed equations involving m-accretive mappings in Banach spaces. We produce an extended Newton-type iterative scheme that converges cubically to the solution which uses assumptions only on the first Fr chet derivative of the operator. Using general H lder type source condition we obtain an error estimate. We also use the adaptive parameter choice strategy proposed by Pereverzev and Schock (SIAM J Numer Anal 43(5):2060 2076, 2005) for choosing the regularization parameter. 2018, Korean Society for Computational and Applied Mathematics.