A Variational Principle in Reflexive Spaces with Kadec-Klee Norm

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F67985840%3A_____%2F09%3A00337028" target="_blank" >RIV/67985840:_____/09:00337028 - isvavai.cz</a>

Result on the web

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DOI - Digital Object Identifier

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Result language

angličtina

Original language name

A Variational Principle in Reflexive Spaces with Kadec-Klee Norm

Original language description

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 waythat 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 thereflexive spaces with Kadec-Klee norm. This principle turns out to be an analytic counterpart of a result of K.-S. Lau on nearest points.

Czech name

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Czech description

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Type

J_x - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)

CEP classification

BA - General mathematics

OECD FORD branch

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Project

<a href="/en/project/GA201%2F04%2F0090" target="_blank" >GA201/04/0090: Geometrical analysis in Banach spaces II</a><br>

Continuities

Z - Vyzkumny zamer (s odkazem do CEZ)

Publication year

2009

Confidentiality

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Name of the periodical

Journal of Convex Analysis

ISSN

0944-6532

e-ISSN

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Volume of the periodical

16

Issue of the periodical within the volume

1

Country of publishing house

DE - GERMANY

Number of pages

16

Pages from-to

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UT code for WoS article

000268197200011

EID of the result in the Scopus database

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