On the Newton-Kantorovich method in \(K\)-normed spaces (Q1851402)
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scientific article; zbMATH DE number 1846802
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the Newton-Kantorovich method in \(K\)-normed spaces |
scientific article; zbMATH DE number 1846802 |
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On the Newton-Kantorovich method in \(K\)-normed spaces (English)
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17 December 2002
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The nonlinear operator equation \( f(x) + g(x) = 0 \) in \(K\)-normed spaces is analysed, where \(f\) is differentiable but \(g\) is not. Here \(K\) is a closed convex regular cone in a real Banach space. Under reasonable assumptions, esp. \(f'\) and \(g\) being Lipschitz in some ball, the authors prove solvability by means of the convergence of a Newton-Kantorovich-type iteration.
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\(K\)-normed space
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nonlinear operator equation
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Newton-Kantorovich iteration
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