On the Convergence and Application of Generalized Newton Methods

In this study under very general conditions we use the generalized Newton method to generate a sequence approximating a locally unique solution of a nonlinear operator equation in a Banach space setting. Using new and more precise majorizing sequences we provide new sufficient conditions for the local and semilocal convergence of the generalized Newton method. It turns out that our error bounds are finer and the information on the location of the solution more precise than before. In the local case we provide a larger convergence radius than before. Finally we provide numerical examples to show that our result apply where others fail.