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Mat. Sb., 1997, Volume 188, Number 12, Pages 33–56 (Mi msb271)  

This article is cited in 14 scientific papers (total in 14 papers)

Topological properties of the set of fixed points of a multivalued map

B. D. Gel'man

Voronezh State University

Abstract: This paper is a study of the topological properties of the set of fixed points of a multivalued map. Some theorems are proved on the topological dimension of this set, and conditions are studied under which the set is connected or acyclic. The theorems obtained are applied to the investigation of the set of solutions of differential and integral inclusions.

DOI: https://doi.org/10.4213/sm271

Full text: PDF file (372 kB)
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English version:
Sbornik: Mathematics, 1997, 188:12, 1761–1782

Bibliographic databases:

UDC: 515.126.83
MSC: Primary 54C60, 54H25, 54C65; Secondary 47H09, 28B20, 55M20, 55M25, 34A60, 55M10
Received: 19.09.1995

Citation: B. D. Gel'man, “Topological properties of the set of fixed points of a multivalued map”, Mat. Sb., 188:12 (1997), 33–56; Sb. Math., 188:12 (1997), 1761–1782

Citation in format AMSBIB
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  • http://mi.mathnet.ru/eng/msb/v188/i12/p33

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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. B. D. Gel'man, “On a Class of Operator Equations”, Math. Notes, 70:4 (2001), 494–501  mathnet  crossref  crossref  mathscinet  zmath  isi  elib
    2. Andres, J, “Acyclicity of solution sets to functional inclusions”, Nonlinear Analysis-Theory Methods & Applications, 49:5 (2002), 671  crossref  mathscinet  zmath  isi  elib  scopus  scopus
    3. V. G. Zvyagin, E. S. Baranovskii, “Topological degree of condensing multi-valued perturbations of the $(S)_+$-class maps and its applications”, Journal of Mathematical Sciences, 170:3 (2010), 405–422  mathnet  crossref  mathscinet
    4. B. D. Gel'man, “On the acyclicity of the solution sets of operator equations”, Sb. Math., 201:10 (2010), 1449–1459  mathnet  crossref  crossref  mathscinet  zmath  adsnasa  isi  elib  elib
    5. Gelman B.D., Zhuk N.M., “O beskonechnomernoi versii teoremy borsuka-ulama dlya mnogoznachnykh otobrazhenii”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2011, no. 2, 78–84  zmath  elib
    6. Rydanova S.S., “Ob odnom klasse operatornykh uravnenii”, Vestnik tambovskogo universiteta. seriya: estestvennye i tekhnicheskie nauki, 16:4 (2011), 1173–1174  elib
    7. Gelman B.D., Rydanova S.S., “Ob operatornykh uravneniyakh s syurektivnymi operatorami”, Vestnik Voronezhskogo gosudarstvennogo universiteta. Seriya: Fizika. Matematika, 2012, no. 1, 93–93  mathscinet  zmath  elib
    8. Radosław Pietkun, “Structure of the solution set to Volterra integral inclusions and applications”, Journal of Mathematical Analysis and Applications, 2013  crossref  mathscinet  isi  scopus  scopus
    9. B. D. Gel'man, “The Solution Set of a Class of Equations with Surjective Operators”, Funct. Anal. Appl., 49:1 (2015), 60–63  mathnet  crossref  crossref  zmath  isi  elib
    10. B. D. Gel'man, “How to Approach Nonstandard Boundary Value Problems”, Funct. Anal. Appl., 50:1 (2016), 31–38  mathnet  crossref  crossref  mathscinet  isi  elib
    11. B. D. Gel'man, “A version of the infinite-dimensional Borsuk-Ulam theorem for multivalued maps”, Sb. Math., 207:6 (2016), 841–853  mathnet  crossref  crossref  mathscinet  adsnasa  isi  elib
    12. Poncet P., “Representation of maxitive measures: An overview”, Math. Slovaca, 67:1 (2017), 121–150  crossref  mathscinet  zmath  isi  scopus
    13. A. V. Arutyunov, E. S. Zhukovskiy, S. E. Zhukovskiy, “On the cardinality of the coincidence set for mappings of metric, normed and partially ordered spaces”, Sb. Math., 209:8 (2018), 1107–1130  mathnet  crossref  crossref  adsnasa  isi  elib
    14. E. S. Zhukovskii, “O svyaznosti mnozhestv reshenii vklyuchenii”, Matem. sb., 210:6 (2019), 82–110  mathnet  crossref
  • Математический сборник - 1992–2005 Sbornik: Mathematics (from 1967)
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