ar X iv : 1 31 1 . 28 15 v 1 [ m at h . FA ] 1 2 N ov 2 01 3 GLOBAL INVERSION OF NONSMOOTH MAPPINGS USING PSEUDO - JACOBIAN MATRICES
نویسنده
چکیده
We study the global inversion of a continuous nonsmooth mapping f : R → R, 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.
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