Some quantitative results on Lipschitz inverse and implicit function theorems

Details Some quantitative results on Lipschitz inverse and implicit function theorems Some quantitative results on Lipschitz inverse and implicit function theorems

2012-04-22

arxiv.org/abs/1204.4916v1

East-West Journal of Mathematics, Vol. 13, No 1 (2011), 7-22

Mathematics

Numerical Analysis

15 pages

Scientific paper

Let $ f: \mathbb{R} ^ n \rightarrow \mathbb{R}^n $ be a Lipschitz mapping with generalized Jacobian at $x_0$, denoted by $\partial f(x_0)$, is of maximal rank. F. H. Clarke (1976) proved that $f$ is locally invertible. In this paper, we give some quantitative assessments for Clarke's theorem on the Lipschitz inverse, and prove that the class of such mappings are open. Moreover, we also present a quantitative form for Lipschitz implicit function theorem.

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