A Newton-type method and its application
2006 ◽
Vol 2006
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pp. 1-9
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Keyword(s):
We prove an existence and uniqueness theorem for solving the operator equationF(x)+G(x)=0, whereFis a continuous and Gâteaux differentiable operator and the operatorGsatisfies 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.
2013 ◽
Vol 33
(5)
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pp. 1305-1313
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2015 ◽
Vol 3
(2)
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pp. 66
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2004 ◽
Vol 2004
(3)
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pp. 271-282
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2009 ◽
Vol 71
(12)
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pp. e1575-e1578
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