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Implicit functions and sensitivity of stationary points. (English) Zbl 0715.65034
The space L(D) consists of Lipschitz continuous mappings from D to the Euclidean n-space $$R^ n$$, D being an open bounded subset of $$R^ n$$. Let F belong to L(D) and suppose that $$\bar x$$ solves the equation $$F(x)=0$$. If the generalized Jacobian (in some particular sense) of F at $$\bar x$$ is nonsingular then it is shown that for G near F (with respect to a natural norm) the system $$G(x)=0$$ has a unique solution x(G) in neighbourhood of $$\bar x$$ and the mapping x to x(G) is Lipschitz continuous.
Reviewer: V.Subba Rao

##### MSC:
 65H10 Numerical computation of solutions to systems of equations 55M25 Degree, winding number
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