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. Sb.:
Year:
Volume:
Issue:
Page:
Find






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


Mat. Sb., 2006, Volume 197, Number 9, Pages 103–114 (Mi msb1492)  

This article is cited in 2 scientific papers (total in 2 papers)

Best approximation problems relating to Monge–Kantorovich duality

V. L. Levin

Central Economics and Mathematics Institute, RAS

Abstract: Problems of the best approximation of bounded continuous functions on a topological space $X\times X$ by functions of the form $u(x)-u(y)$ are considered. Formulae for the values of the best approximations are obtained and the equivalence between the existence of precise solutions and the non-emptiness of the constraint set of the auxiliary dual Monge–Kantorovich problem with a special cost function is established. The form of precise solutions is described in terms relating to the Monge–Kantorovich duality, and for several classes of approximated functions the existence of precise solutions with additional properties, such as smoothness and periodicity, is proved.
Bibliography: 20 titles.

DOI: https://doi.org/10.4213/sm1492

Full text: PDF file (515 kB)
References: PDF file   HTML file

English version:
Sbornik: Mathematics, 2006, 197:9, 1353–1364

Bibliographic databases:

UDC: 517.972.8
MSC: 41A50, 49N15
Received: 12.01.2006

Citation: V. L. Levin, “Best approximation problems relating to Monge–Kantorovich duality”, Mat. Sb., 197:9 (2006), 103–114; Sb. Math., 197:9 (2006), 1353–1364

Citation in format AMSBIB
\Bibitem{Lev06}
\by V.~L.~Levin
\paper Best approximation problems
relating to Monge--Kantorovich duality
\jour Mat. Sb.
\yr 2006
\vol 197
\issue 9
\pages 103--114
\mathnet{http://mi.mathnet.ru/msb1492}
\crossref{https://doi.org/10.4213/sm1492}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=2273170}
\zmath{https://zbmath.org/?q=an:1151.41019}
\elib{http://elibrary.ru/item.asp?id=9277055}
\transl
\jour Sb. Math.
\yr 2006
\vol 197
\issue 9
\pages 1353--1364
\crossref{https://doi.org/10.1070/SM2006v197n09ABEH003802}
\isi{http://gateway.isiknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=PARTNER_APP&SrcAuth=LinksAMR&DestLinkType=FullRecord&DestApp=ALL_WOS&KeyUT=000243495000006}
\elib{http://elibrary.ru/item.asp?id=13769853}
\scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-33846495786}


Linking options:
  • http://mi.mathnet.ru/eng/msb1492
  • https://doi.org/10.4213/sm1492
  • http://mi.mathnet.ru/eng/msb/v197/i9/p103

    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. Levin V.L., “Smooth feasible solutions to a dual Monge-Kantorovich problem and their application to the best approximation and mathematical economics problems”, Dokl. Math., 77:2 (2008), 281–283  mathnet  crossref  mathscinet  zmath  isi  elib  elib
    2. Levin V.L., “Dvoistvennost Monzha–Kantorovicha i ee primenenie v teorii poleznosti”, Ekonomika i matematicheskie metody, 47:4 (2011), 143–165  elib
  • Математический сборник Sbornik: Mathematics (from 1967)
    Number of views:
    This page:323
    Full text:125
    References:44
    First page:1

     
    Contact us:
     Terms of Use  Registration  Logotypes © Steklov Mathematical Institute RAS, 2019