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Matematicheskie Zametki, 2012, Volume 91, Issue 1, Pages 74–78
DOI: https://doi.org/10.4213/mzm8907 (Mi mzm8907) 		 
This article is cited in 1 scientific paper (total in 1 paper)

A Construction of Convex Functions

T. Konderla

Mathematical Institute, Silesian University in Opava, Opava, Czech Republic
Full-text PDF (408 kB) Citations (1)
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DOI: https://doi.org/10.4213/mzm8907
Abstract: We describe a construction of convex functions on infinite-dimensional spaces and apply this construction to give an illustration to a theorem of Borwein–Fabian from [1]. Namely, we give a simple explicit example of a continuous convex function on $l_p$, $p\ge 1$, which is everywhere compactly differentiable, but not Fréchet differentiable at zero.
Keywords: topological vector space, normed space, convex function, Fréchet differentiability, Gâteaux differentiability, compact differentiability.
Received: 13.04.2009
English version:
Mathematical Notes, 2012, Volume 91, Issue 1, Pages 65–68
DOI: https://doi.org/10.1134/S0001434612010075
Bibliographic databases:
Document Type: Article
UDC: 517.2+517.98
Language: Russian
Citation: T. Konderla, “A Construction of Convex Functions”, Mat. Zametki, 91:1 (2012), 74–78; Math. Notes, 91:1 (2012), 65–68
Citation in format AMSBIB
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  • https://www.mathnet.ru/eng/mzm/v91/i1/p74
    • This publication is cited in the following 1 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Математические заметки Mathematical Notes
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