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A note on Robinson-Ursescu and Lyusternik-Graves theorem
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SYSNO ASEP 0395288 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A note on Robinson-Ursescu and Lyusternik-Graves theorem Author(s) Cibulka, R. (CZ)
Fabian, Marián (MU-W) RID, SAI, ORCIDSource Title Mathematical Programming. - : Springer - ISSN 0025-5610
Roč. 139, 1-2 (2013), s. 89-101Number of pages 13 s. Language eng - English Country NL - Netherlands Keywords open mapping ; restrictive metricregularity ; graves theorem Subject RIV BA - General Mathematics R&D Projects GAP201/11/0345 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000320844200007 EID SCOPUS 84879696604 DOI 10.1007/s10107-013-0662-z Annotation The aim of this note is twofold. First, we prove an analogue of the well-known Robinson–Ursescu Theorem on the relative openness with a linear rate (restrictive metric regularity) of a multivalued mapping. Second, we prove a generalization of Graves Open Mapping Theorem for a class of mappings which can be approximated at a reference point by a bunch of linear mappings. The approximated non-linear mapping is restricted to a closed convex subset of a Banach space. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2014
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