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Trudy Inst. Mat. i Mekh. UrO RAN, 2011, Volume 17, Number 2, Pages 225–239 (Mi timm709)  

This article is cited in 5 scientific papers (total in 5 papers)

One representation of the results of action of approximate solutions in a problem with constraints of asymptotic nature

A. G. Chentsov

Institute of Mathematics and Mechanics, Ural Branch of the Russian Academy of Sciences

Abstract: We consider an abstract attainability problem with constraints of asymptotic nature defined in the form of a nonempty family of subsets in the space of usual solutions. Various variants of implementing asymptotic effects are considered (convergence in a topological space, cycles, and so on). A rather general method is suggested for presenting the results of action of approximate solutions; this method generalizes constructions based on sequences in the space of usual solutions.

Keywords: attraction set, net, ultrafilter.

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English version:
Proceedings of the Steklov Institute of Mathematics (Supplementary issues), 2012, 276, suppl. 1, S48–S62

Bibliographic databases:

Document Type: Article
UDC: 519.6
Received: 22.11.2010

Citation: A. G. Chentsov, “One representation of the results of action of approximate solutions in a problem with constraints of asymptotic nature”, Trudy Inst. Mat. i Mekh. UrO RAN, 17, no. 2, 2011, 225–239; Proc. Steklov Inst. Math. (Suppl.), 276, suppl. 1 (2012), S48–S62

Citation in format AMSBIB
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\paper One representation of the results of action of approximate solutions in a~problem with constraints of asymptotic nature
\serial Trudy Inst. Mat. i Mekh. UrO RAN
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\pages 225--239
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\jour Proc. Steklov Inst. Math. (Suppl.)
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\pages S48--S62
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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. A. G. Chentsov, “Yarusnye otobrazheniya i preobrazovaniya na osnove ultrafiltrov”, Tr. IMM UrO RAN, 18, no. 4, 2012, 298–314  mathnet  elib
    2. A. G. Chentsov, “On the question of representation of ultrafilters in a product of measurable spaces”, Proc. Steklov Inst. Math. (Suppl.), 284, suppl. 1 (2014), 65–78  mathnet  crossref  mathscinet  isi  elib
    3. A. G. Chentsov, “On the question of representation of ultrafilters and their application in extension constructions”, Proc. Steklov Inst. Math. (Suppl.), 287, suppl. 1 (2014), 29–48  mathnet  crossref  mathscinet  isi  elib
    4. A. G. Chentsov, “On certain problems of the structure of ultrafilters related to extensions of abstract control problems”, Autom. Remote Control, 74:12 (2013), 2020–2036  mathnet  crossref  isi
    5. A. G. Chentsov, “Ultrafiltry izmerimykh prostranstv i ikh primenenie v konstruktsiyakh rasshirenii”, Tr. IMM UrO RAN, 20, no. 1, 2014, 285–304  mathnet  mathscinet  elib
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