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Algebraic Univalence Theorems for Nonsmooth Functions

✍ Scribed by M.Seetharama Gowda; G Ravindran

Publisher: Elsevier Science
Year: 2000
Tongue: English
Weight: 130 KB
Volume: 252
Category: Article
ISSN: 0022-247X
DOI: 10.1006/jmaa.2000.7171

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✦ Synopsis

Ann. 159, 81᎐93 asserts that if the Jacobian matrix of a differentiable function from a closed rectangle K in R n into R n is a P-matrix at each point of K, then f is one-to-one on K. In this paper, by introducing the concepts of H-differentiabil-Ž . ity and H-differential of a function as a set of matrices , we generalize the Gale᎐Nikaido result to nonsmooth functions. Our results further extend those of other authors valid for compact rectangles. We show that our results are applicable when the H-differential is any one of the following: the Jacobian matrix of a differentiable function, the generalized Jacobian of a locally Lipschitzian function, the Bouligand subdifferential of a semismooth function, and the C-differential of Ž .

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