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Global inversion of nonsmooth mappings using pseudo-Jacobian matrices
- Publication Year :
- 2013
-
Abstract
- We study the global inversion of a continuous nonsmooth mapping $f: \mathbb{R}^n \rightarrow \mathbb{R}^n$, which may be non-locally Lipschitz. To this end, we use the notion of pseudo-Jacobian map associated to f, introduced by Jeyakumar and Luc, and we consider a related index of regularity for f. We obtain a characterization of global inversion in terms of its index of regularity. Furthermore, we prove that the Hadamard integral condition has a natural counterpart in this setting, providing a sufficient condition for global invertibility.<br />Comment: 12 pages
- Subjects :
- Mathematics - Functional Analysis
49J52, 49J53
Subjects
Details
- Database :
- arXiv
- Publication Type :
- Report
- Accession number :
- edsarx.1311.2815
- Document Type :
- Working Paper