The Newton-Kantorovich approximations for nonlinear singular integral equations with shift (Q1425609)
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scientific article; zbMATH DE number 2059956
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | The Newton-Kantorovich approximations for nonlinear singular integral equations with shift |
scientific article; zbMATH DE number 2059956 |
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The Newton-Kantorovich approximations for nonlinear singular integral equations with shift (English)
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17 March 2004
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Nonlinear singular integral equations with Carleman shift are considered in generalized Hölder spaces. The author proves convergence of the Newton-Kantorovich approximation for a class of singular integral equations for which the Fréchet derivative of the underlying nonlinear operator is locally Lipschitz continuous. Moreover, conditions sufficient for the local Lipschitz continuity of the derivative are provided.
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Newton-Kantorovich method
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singular integral equation
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Carleman shift
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convergence
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generalized Hölder spaces
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