Newton-Kantorovich iterative regularization and generalized discrepancy principle for nonlinear ill-posed equations involving accretive mappings

Abstract

In this paper, in order to solve nonlinear ill-posed operator equations involving an m-accretive mapping on a real Banach space, that does not admit a weak sequential continuous duality mapping, we prove a strongly convergent theorem for Newton-Kantorovich iterative regularization method with a posteriori stopping rule. In our results, the Lipschitz continuity of the derivatives for the mapping is not necessary.