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Mat. Sb., 1996, Volume 187, Number 5, Pages 121–142 (Mi msb131)  

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

Continuous selections of multivalued maps with non-convex non-closed decomposable values

A. A. Tolstonogov

Institute of System Dynamics and Control Theory, Siberian Branch of the Russian Academy of Sciences

Abstract: A class of multivalued maps with non-convex non-closed decomposable values is distinguished, and theorems are proved on the existence of continuous selections for such maps. This class contains multivalued maps whose values are extreme points of continuous multivalued maps with closed convex decomposable values in a Banach space of Bochner-integrable functions. The proofs are based on the Baire category theorem. It is known that the set of extreme points of a closed convex set is in general not closed. Hence the results or paper answer the question of the existence of continuous selections for multivalued maps with non-convex non-closed values.

DOI: https://doi.org/10.4213/sm131

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English version:
Sbornik: Mathematics, 1996, 187:5, 745–766

Bibliographic databases:

UDC: 517.965
MSC: Primary 54C65, 54C60; Secondary 34A40, 28B20
Received: 12.01.1995 and 13.11.1995

Citation: A. A. Tolstonogov, “Continuous selections of multivalued maps with non-convex non-closed decomposable values”, Mat. Sb., 187:5 (1996), 121–142; Sb. Math., 187:5 (1996), 745–766

Citation in format AMSBIB
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  • https://doi.org/10.4213/sm131
  • http://mi.mathnet.ru/eng/msb/v187/i5/p121

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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Tolstonogov, AA, “L-p-continuous selections of fixed points of multifunctions with decomposable values. I: Existence theorems”, Siberian Mathematical Journal, 40:3 (1999), 695-709  mathnet  crossref  mathscinet  zmath  isi  scopus  scopus  scopus
    2. A. A. Tolstonogov, “Properties of the set of admissible “state-control” pairs for first-order evolution control systems”, Izv. Math., 65:3 (2001), 617–640  mathnet  crossref  crossref  mathscinet  zmath  elib
    3. Siberian Math. J., 43:4 (2002), 731–745  mathnet  crossref  mathscinet  zmath  isi  scopus
    4. Li, GC, “On the periodic solutions of differential inclusions and applications”, Applied Mathematics and Mechanics-English Edition, 25:2 (2004), 168  crossref  mathscinet  isi
    5. Tolstonogov, AA, “Existence and relaxation theorems for extreme continuous selectors of multifunctions with decomposable values”, Topology and Its Applications, 155:8 (2008), 898  crossref  mathscinet  zmath  isi  elib  scopus  scopus  scopus
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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