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