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- W2005874105 abstract "In this note we use the Newton-Raphson approach to inverse function theorems. We draw natural conclusions when only a left or a right inverse to the differential at a point is available. By using a strengthened version of differential, we are able to use differentiability at a single point as the smoothness condition. Although the method has been used before (cf. [2, p. 167 ff.]), analysis books have tended to use an approach that assumes finite dimensionality of the reference spaces. DEFINITION. Let U and V be Banach spaces and f: U-* V a function. A strong differential of f at a point xO in U is a bounded linear transformation a: U-* V which approximates changes of f in the sense that for every E> 0, there is a 5 >0 such that if x' and x are nearer than a to 0, then:" @default.
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- W2005874105 date "1961-05-01" @default.
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- W2005874105 title "A note on inverse function theorems" @default.
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- W2005874105 doi "https://doi.org/10.1090/s0002-9939-1961-0126146-9" @default.
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