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A Variational Principle in Reflexive Spaces with Kadec-Klee Norm
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SYSNO ASEP 0337028 Document Type J - Journal Article R&D Document Type Journal Article Subsidiary J Článek ve WOS Title A Variational Principle in Reflexive Spaces with Kadec-Klee Norm Title Variační princip v reflexních prostorech s Kadecovou-Kleeovou normou Author(s) Fabian, Marián (MU-W) RID, SAI, ORCID
Revalski, J. P. (BN)Source Title Journal of Convex Analysis. - : Heldermann Verlag - ISSN 0944-6532
Roč. 16, č. 1 (2009), s. 211-226Number of pages 16 s. Language eng - English Country DE - Germany Keywords reflexive space ; Kadec-Klee norm ; variational principle ; perturbed function ; well-posed infimum Subject RIV BA - General Mathematics R&D Projects GA201/04/0090 GA ČR - Czech Science Foundation (CSF) CEZ AV0Z10190503 - MU-W (2005-2011) UT WOS 000268197200011 Annotation We prove a variational principle in reflexive Banach spaces X with Kadec-Klee norm, which asserts that any Lipschitz (or any proper lower semicontinuous bounded from below extended real-valued) function in X can be perturbed with a parabola in such a way that the perturbed function attains its infimum (even more can be said - the infimum is well-posed). In addition, we have genericity of the points determining the parabolas. We prove also that the validity of such a principle actually characterizes the reflexive spaces with Kadec-Klee norm. This principle turns out to be an analytic counterpart of a result of K.-S. Lau on nearest points. Workplace Mathematical Institute Contact Jarmila Štruncová, struncova@math.cas.cz, library@math.cas.cz, Tel.: 222 090 757 Year of Publishing 2010
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