Convergence of Newton's method and uniqueness of the solution of equations in Banach spaces. II (Q1396024)

The authors continue their work on the Newton-Kantorowitsch method for solving nonlinear equations in a Banach space. Convergence and uniqueness results are studied under the assumption that the operator's derivative fulfills a so-called radius or center Lipschitz condition with the weak \(L\) average. Part I of this work has been published by \textit{X. Wang} [IMA J. Numer. Anal. 20, No. 1, 123-134 (2000; Zbl 0942.65057)]. The reader should also consult \textit{X. Wang, C. Li,} and \textit{M.-J. Lai} [BIT 42, 206-213 (2002; Zbl 0998.65057)].