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Isolated zeros of Lipschitzian metrically regular ℝn-functions

Fusek, Peter (2001). Isolated zeros of Lipschitzian metrically regular ℝn-functions. Optimization, 49(5-6):425-446.

Abstract

Given a metrically regular locally Lipschitzian function sending $_{ℝn}$ into $_{ℝm}$,the structure of the preimages will be studied. In particular, for the case of m =n, it will be shown that all preimages are locally finite sets provided that the Lipschitzian function in question is directionally differentiable. Some consequences of this fact will be discussed.

Additional indexing

Item Type:Journal Article, refereed, original work
Communities & Collections:07 Faculty of Science > Institute of Mathematics
Dewey Decimal Classification:510 Mathematics
Scopus Subject Areas:Physical Sciences > Control and Optimization
Social Sciences & Humanities > Management Science and Operations Research
Physical Sciences > Applied Mathematics
Uncontrolled Keywords:Inverse (Multi-)Functions, Isolated Zeros, Metric Regularity, Nonsmooth Equations, Pseudo-Lipschitz Property
Language:English
Date:2001
Deposited On:29 Nov 2010 16:27
Last Modified:03 Jun 2025 01:36
Publisher:Taylor & Francis
ISSN:0233-1934
Additional Information:This is an electronic version of an article published in "Optimization" 49: 5-6, pages 452-446 is available online at:https://doi.org/10.1080/02331930108844542
OA Status:Closed
Publisher DOI:https://doi.org/10.1080/02331930108844542
Related URLs:http://www.ams.org/mathscinet-getitem?mr=1891077
http://www.zentralblatt-math.org/zbmath/search/?q=an%3A0987.49009

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