Lavrentiev's regularization method for nonlinear ill-posed equations in Banach spaces

Abstract

In this paper, we deal with nonlinear ill-posed problems involving m-accretive mappings in Banach spaces. We consider a derivative and inverse free method for the implementation of Lavrentiev regularization method. Using general Hölder type source condition we obtain an optimal order error estimate. Also we consider the adaptive parameter choice strategy proposed by Pereverzev and Schock (2005) for choosing the regularization parameter. © 2018 Wuhan Institute of Physics and Mathematics