Smulyan Lemma and Differentiability of the Support Function

The purpose of this paper is to verify the Smulyan lemma for the support function,and also the Gateaux differentiability of the support function is studied on its domain.Moreover,we provide a characterization of Frechet differentiability of the support function on the extremal points.

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Bibliographic Details
Published inAnalysis in theory & applications Vol. 34; no. 4; pp. 348 - 357
Main Author Hassankhali, Ildar Sadeqi & Sima
Format Journal Article
LanguageEnglish
Published Department of Mathematics, Sahand University of Technology, Tabriz-Iran 01.06.2018
Subjects
strict convexity
Frechet and Gateaux differentiability
Smulyan lemma
support function
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Summary:The purpose of this paper is to verify the Smulyan lemma for the support function,and also the Gateaux differentiability of the support function is studied on its domain.Moreover,we provide a characterization of Frechet differentiability of the support function on the extremal points.
ISSN:1672-4070
1573-8175
DOI:10.4208/ata.OA-2017-0024