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- W2531699496 abstract "A function from one normed linear space to another is said to be Bouligand differentiable (B-differentiable) at a point if it is directionally differentiable there in every direction, and if the directional derivative has a certain uniformity property. This is a weakening of the classical idea of Frechet (F-) differentiability, and it is useful in dealing with optimization problems and in other situations in which F-differentiability may be too strong. In this paper we introduce a concept of strong B-derivative, and we employ this idea to prove an implicit-function theorem for B-differentiable functions. This theorem provides the same kinds of information as does the classical implicit-function theorem, but with B-differentiability in place of F-differentiability. Therefore it is applicable to a considerably wider class of functions than is the classical theorem." @default.
- W2531699496 created "2016-10-21" @default.
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- W2531699496 date "1988-07-01" @default.
- W2531699496 modified "2023-09-26" @default.
- W2531699496 title "An Implicit-Function Theorem for B-Differentiable Functions" @default.
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