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Mat. Zametki, 1968, Volume 4, Issue 6, Pages 685–696 (Mi mz6789)  

This article is cited in 6 scientific papers (total in 6 papers)

Some properties of support functionals

V. L. Levin

Central Economics and Mathematics Institute, USSR Academy of Sciences

Abstract: The author considers convex functionals $f_t$ defined on the open convex subset $G$ of real $B$-space $X$ and continuous at $x_0\in G$. All linear functionals on $X$ which are support functionals of form $\int_Tf_t(x)\mu(dt)$ and $\max\limits_{t\in T}f_t(x)$ at $x_0$ are described.

Full text: PDF file (927 kB)

English version:
Mathematical Notes, 1968, 4:6, 900–906

Bibliographic databases:

UDC: 513.88
Received: 09.01.1968

Citation: V. L. Levin, “Some properties of support functionals”, Mat. Zametki, 4:6 (1968), 685–696; Math. Notes, 4:6 (1968), 900–906

Citation in format AMSBIB
\Bibitem{Lev68}
\by V.~L.~Levin
\paper Some properties of support functionals
\jour Mat. Zametki
\yr 1968
\vol 4
\issue 6
\pages 685--696
\mathnet{http://mi.mathnet.ru/mz6789}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=450948}
\zmath{https://zbmath.org/?q=an:0183.15703}
\transl
\jour Math. Notes
\yr 1968
\vol 4
\issue 6
\pages 900--906
\crossref{https://doi.org/10.1007/BF01110826}


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    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. V. L. Levin, “Application of E. Helly's theorem to convex programming, problems of best approximation and related questions”, Math. USSR-Sb., 8:2 (1969), 235–247  mathnet  crossref  mathscinet  zmath
    2. A. D. Ioffe, “Subdifferentsialy ogranichenii vypuklykh funktsii”, UMN, 25:4(154) (1970), 181–182  mathnet  mathscinet  zmath
    3. V. L. Levin, “O subdifferentsialakh vypuklykh funktsionalov”, UMN, 25:4(154) (1970), 183–184  mathnet  mathscinet  zmath
    4. V. L. Levin, “Convex integral functionals and the theory of lifting”, Russian Math. Surveys, 30:2 (1975), 119–184  mathnet  crossref  mathscinet  zmath
    5. V. N. Solov'ev, “The subdifferential and the directional derivatives of the maximum of a family of convex functions”, Izv. Math., 62:4 (1998), 807–832  mathnet  crossref  crossref  mathscinet  zmath  isi
    6. V. N. Solov'ev, “The subdifferential and the directional derivatives of the maximum of a family of convex functions. II”, Izv. Math., 65:1 (2001), 99–121  mathnet  crossref  crossref  mathscinet  zmath
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