RUS  ENG JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB
General information
Latest issue
Forthcoming papers
Archive
Impact factor
Subscription
Guidelines for authors
License agreement
Submit a manuscript

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS



Mat. Zametki:
Year:
Volume:
Issue:
Page:
Find






Personal entry:
Login:
Password:
Save password
Enter
Forgotten password?
Register


Mat. Zametki, 2012, Volume 91, Issue 1, Pages 74–78 (Mi mz8907)  

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

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

DOI: https://doi.org/10.4213/mzm8907

Full text: PDF file (408 kB)
References: PDF file   HTML file

English version:
Mathematical Notes, 2012, 91:1, 65–68

Bibliographic databases:

UDC: 517.2+517.98
Received: 13.04.2009

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
\Bibitem{Kon12}
\by T.~Konderla
\paper A Construction of Convex Functions
\jour Mat. Zametki
\yr 2012
\vol 91
\issue 1
\pages 74--78
\mathnet{http://mi.mathnet.ru/mz8907}
\crossref{https://doi.org/10.4213/mzm8907}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=3201394}
\elib{http://elibrary.ru/item.asp?id=20731465}
\transl
\jour Math. Notes
\yr 2012
\vol 91
\issue 1
\pages 65--68
\crossref{https://doi.org/10.1134/S0001434612010075}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000303478400007}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84857577949}


Linking options:
  • http://mi.mathnet.ru/eng/mz8907
  • https://doi.org/10.4213/mzm8907
  • http://mi.mathnet.ru/eng/mz/v91/i1/p74

    SHARE: VKontakte.ru FaceBook Twitter Mail.ru Livejournal Memori.ru


    Citing articles on Google Scholar: Russian citations, English citations
    Related articles on Google Scholar: Russian articles, English articles

    This publication is cited in the following articles:
    1. E. M. Bednarczuk, K. Lesniewski, “On weakly sequentially complete Banach spaces”, J. Convex Anal., 24:4 (2017), 1341–1356  mathscinet  zmath  isi
  • Математические заметки Mathematical Notes
    Number of views:
    This page:278
    Full text:89
    References:42
    First page:11

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2020