International Journal of Mathematics and Mathematical Sciences
Volume 2006 (2006), Article ID 23674, 9 pages
A Newton-type method and its application
Department of Mathematics, Indian Institute of Technology Madras, Chennai 600036, India
Received 6 March 2006; Accepted 26 March 2006
Copyright © 2006 V. Antony Vijesh and P. V. Subrahmanyam. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We prove an existence and uniqueness theorem for solving the
operator equation , where
is a continuous and
Gâteaux differentiable operator and the operator
Lipschitz condition on an open convex subset of a Banach space. As
corollaries, a recent theorem of Argyros (2003) and the classical
convergence theorem for modified Newton iterates are deduced. We
further obtain an existence theorem for a class of nonlinear
functional integral equations involving the Urysohn operator.