On the Convergence of Stirling s Method for Fixed Points Under Not Necessarily Contractive Hypotheses

Abstract

Stirling s method is a useful alternative to Newton s method for approximating fixed points of nonlinear operators in a Banach space setting. This method has been studied under contractive hypotheses on the operator involved, thus limiting the applicability of it. In this study, we present a local as well as a semi-local convergence for this method based on not necessarily contractive hypotheses. This way, we extend the applicability of the method. Moreover, we present a favorable comparison of the new Kantorovich-type convergence criteria with the old ones using contractive hypotheses as well as with Newton s method. Numerical examples including Hammerstein nonlinear equations of Chandrasekar type appearing in neutron transport and in the kinetic theory of gases are solved to further illustrate the theoretical results. 2017, Springer (India) Private Ltd.