Loading [MathJax]/jax/output/SVG/config.js
Trudy Instituta Matematiki i Mekhaniki UrO RAN
RUS  ENG    JOURNALS   PEOPLE   ORGANISATIONS   CONFERENCES   SEMINARS   VIDEO LIBRARY   PACKAGE AMSBIB  
General information
Latest issue
Archive
Impact factor

Search papers
Search references

RSS
Latest issue
Current issues
Archive issues
What is RSS


Trudy Inst. Mat. i Mekh. UrO RAN:
Year:
Volume:
Issue:
Page:
Find




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

Trudy Instituta Matematiki i Mekhaniki UrO RAN, 2019, Volume 25, Number 3, Pages 232–246
DOI: https://doi.org/10.21538/0134-4889-2019-25-3-232-246 (Mi timm1661) 		 
This article is cited in 1 scientific paper (total in 1 paper)

On the Construction of a Nonanticipating Selection of a Multivalued Mapping

D. A. Serkovab, A. G. Chentsovab

a Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences, Ekaterinburg
b Ural Federal University named after the First President of Russia B. N. Yeltsin, Ekaterinburg
Full-text PDF (269 kB) Citations (1)
References:
PDF
HTML
DOI: https://doi.org/10.21538/0134-4889-2019-25-3-232-246
Abstract: We study the properties of multivalued mappings of general form with respect to the possibility of finding their nonanticipating selections. The property of nonanticipation is formulated for an arbitrary domain by specifying some family of “test” subsets. Sufficient conditions for the existence of a nonanticipating selection of a nonanticipating multivalued mapping are proposed: the values of the mapping must be nonempty compact sets, and the family of “test” subsets must be totally ordered with respect to inclusion. We illustrate the results by showing their applicability to the pursuit–evasion differential game in the form of P. Varaya and J. Lin.
Keywords: quasistrategy, nonanticipation, selection, topology.
Funding agency Grant number
Russian Academy of Sciences - Federal Agency for Scientific Organizations
This work was supported by the Presidium of the Russian Academy of Sciences within the project “Newest Methods of Mathematical Modeling in the Study of Nonlinear Dynamic Systems.”
Received: 15.05.2019
Revised: 19.06.2019
Accepted: 24.06.2019
English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2020, Volume 309, Issue 1, Pages S125–S138
DOI: https://doi.org/10.1134/S008154382004015X
Bibliographic databases:
Document Type: Article
UDC: 517.977
Language: Russian
Citation: D. A. Serkov, A. G. Chentsov, “On the Construction of a Nonanticipating Selection of a Multivalued Mapping”, Trudy Inst. Mat. i Mekh. UrO RAN, 25, no. 3, 2019, 232–246; Proc. Steklov Inst. Math. (Suppl.), 309, suppl. 1 (2020), S125–S138
Citation in format AMSBIB
\Bibitem{SerChe19}
\by D.~A.~Serkov, A.~G.~Chentsov
\paper On the Construction of a Nonanticipating Selection of a Multivalued Mapping
\serial Trudy Inst. Mat. i Mekh. UrO RAN
\yr 2019
\vol 25
\issue 3
\pages 232--246
\mathnet{http://mi.mathnet.ru/timm1661}
\crossref{https://doi.org/10.21538/0134-4889-2019-25-3-232-246}
\elib{https://elibrary.ru/item.asp?id=39323551}
\transl
\jour Proc. Steklov Inst. Math. (Suppl.)
\yr 2020
\vol 309
\issue , suppl. 1
\pages S125--S138
\crossref{https://doi.org/10.1134/S008154382004015X}
\isi{https://gateway.webofknowledge.com/gateway/Gateway.cgi?GWVersion=2&SrcApp=Publons&SrcAuth=Publons_CEL&DestLinkType=FullRecord&DestApp=WOS_CPL&KeyUT=000485178300019}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85078514167}
Linking options:
  • https://www.mathnet.ru/eng/timm1661
  • https://www.mathnet.ru/eng/timm/v25/i3/p232
    • This publication is cited in the following 1 articles:
    1. D. A. Serkov, “On the construction of partially non-anticipative multiselector and its application to dynamic optimization problems”, Vestn. Udmurtsk. un-ta. Matem. Mekh. Kompyut. nauki, 34:3 (2024), 410–434  mathnet  crossref
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    		Trudy Instituta Matematiki i Mekhaniki UrO RAN
    Statistics & downloads:
    Abstract page:283
    Full-text PDF :79
    References:52
    First page:1
     
      Contact us:
    math-net2025_05@mi-ras.ru     		 Terms of Use  Registration to the website  Logotypes © Steklov Mathematical Institute RAS, 2025