Theorems on estimates in the neighborhood of a singular point of a mapping (Q757814)
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scientific article; zbMATH DE number 4194536
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Theorems on estimates in the neighborhood of a singular point of a mapping |
scientific article; zbMATH DE number 4194536 |
Statements
Theorems on estimates in the neighborhood of a singular point of a mapping (English)
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1990
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Let \(F:X\to Y\) be a mapping between Banach spaces X and Y, \(x_*\in X\) a given point and U a neighborhood of \(x_*\). If \(M(x_*)=\{x\in U:\;F(x)=F(x_*)\}\) various estimates of the distance \(\rho\) (x,M(x)) by \(\| F(x)-F(x_*)\|\) are derived in the work. An implicit function theorem is derived as a consequence.
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implicit function theorem
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