Solution of a problem of S. Marcus concerning Jensen-convex functions

This paper is devoted to the problem of characterizing the class $ \cal S $ of the stationary sets for J-convex functions $ \Delta \to {\Bbb R} $, where $ \Delta $ is a convex open subset of $ {\Bbb R}^n $. We prove, among others, that a set T belongs to the class $ \cal S $ if and only if T satisfi...

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Bibliographic Details
Published in:Aequationes mathematicae 2002-02, Vol.63 (1-2), p.136-139
Main Author: Babilonová-Štefánková, M.
Format: Article
Language:English
Subjects:
Calculus
Online Access:Get full text
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Summary:This paper is devoted to the problem of characterizing the class $ \cal S $ of the stationary sets for J-convex functions $ \Delta \to {\Bbb R} $, where $ \Delta $ is a convex open subset of $ {\Bbb R}^n $. We prove, among others, that a set T belongs to the class $ \cal S $ if and only if T satisfies two conditions: the closure of the convex hull of T in the relative topology is the whole set $ \Delta $, and each J-convex function bounded above on T is continuous. [PERIODICAL ABSTRACT]
ISSN:0001-9054
1420-8903
DOI:10.1007/s00010-002-8011-y