A Newton-type method and its application

V. Antony Vijesh and P. V. Subrahmanyam

International Journal of Mathematics and Mathematical Sciences, 2006, vol. 2006, 1-9

Abstract:

We prove an existence and uniqueness theorem for solving the operator equation F ( x ) + G ( x ) = 0 , where F is a continuous and Gâteaux differentiable operator and the operator G satisfies 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.

Date: 2006
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jijmms:023674

DOI: 10.1155/IJMMS/2006/23674

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