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Sbornik: Mathematics, 2010, Volume 201, Issue 10, Pages 1449–1459
DOI: https://doi.org/10.1070/SM2010v201n10ABEH004117 (Mi sm7514) 		 
On the acyclicity of the solution sets of operator equations

B. D. Gel'man

Voronezh State University
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DOI: https://doi.org/10.1070/SM2010v201n10ABEH004117
Abstract: A parameter-dependent completely continuous map is considered. The acyclicity of the set of fixed points of this map is proved for some fixed value of the parameter under the assumption that for close values of the parameter the map has a unique fixed point. The results obtained are used to prove the acyclicity of the set of fixed points of a ‘nonscattering’ map, as well as to study the topological structure of the set of fixed points of an abstract Volterra map.
Bibliography: 13 titles.
Keywords: acyclic set, fixed point, completely continuous map.
Received: 10.12.2008 and 12.04.2010
Russian version:
Matematicheskii Sbornik, 2010, Volume 201, Number 10, Pages 47–58
DOI: https://doi.org/10.4213/sm7514
Bibliographic databases:
Document Type: Article
UDC: 517.988.6
MSC: 47J05, 47H10
Language: English
Original paper language: Russian
Citation: B. D. Gel'man, “On the acyclicity of the solution sets of operator equations”, Mat. Sb., 201:10 (2010), 47–58; Sb. Math., 201:10 (2010), 1449–1459
Citation in format AMSBIB
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    		Математический сборник Sbornik: Mathematics
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    Abstract page:467
    Russian version PDF:192
    English version PDF:7
    References:67
    First page:15
     
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