Abstract
The aim of this paper is to study the convergence of Stirling's method used for finding fixed points of nonlinear operator equations assuming that the first Frechet derivative of the nonlinear operator be ω-conditioned. The ω-condition relaxes the Lipschitz/Holder condition on the first Frechet derivative used earlier for the convergence. The existence and uniqueness regions are derived for the fixed points. Finally, the efficacy of our convergence analysis is shown by working out an integral equation of Hammerstein type of second kind. The results obtained show that our approach finds better results when compared with the results obtained by Newton's method. Copyright © 2009 John Wiley & Sons, Ltd.
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