Convergence of Stirling's method under weak differentiability condition

Abstract

The aim of this paper is to establish the semilocal convergence analysis of Stirling's method used to find fixed points of nonlinear operator equations in Banach spaces. This is done by using recurrence relations under weak Holder continuity condition on the first Frechet derivative of the involved operator. The existence and uniqueness regions for a fixed point are obtained. The efficacy of our work is demonstrated by solving an integral equation of Hammerstein type and comparing the results obtained by Newton's method. It is found that our approach gives better existence and uniqueness regions for a fixed point. Copyright © 2010 John Wiley & Sons, Ltd.