On the approximate solutions of nonlinear functional equations under mild differentiability conditions (Q1187282)
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scientific article; zbMATH DE number 39057
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the approximate solutions of nonlinear functional equations under mild differentiability conditions |
scientific article; zbMATH DE number 39057 |
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On the approximate solutions of nonlinear functional equations under mild differentiability conditions (English)
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28 June 1992
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Let \(X\) be a Banach space, \(F\) be a Fréchet differentiable mapping defined on some closed sphere \(S(x_ 0,r)\) in \(X\) and \(F(x)\) in \(\mathbb{R}\) for every \(x\) in \(S(x_ 0,r)\). The author proves some existence results for the equation \(F(x)=0\), where \(F'\) is only Hölder continuous.
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nonlinear functional equation
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Newton's method
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Banach space
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Fréchet differentiable mapping
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