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Sbornik: Mathematics, 2014, Volume 205, Issue 12, Pages 1775–1786
DOI: https://doi.org/10.1070/SM2014v205n12ABEH004439 (Mi sm8386) 		 
This article is cited in 3 scientific papers (total in 3 papers)

Convexity properties of images under nonlinear integral operators

M. Yu. Kokurin

Mari State University, Ioshkar-Ola
English version PDF (458 kB) Citations (3)
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DOI: https://doi.org/10.1070/SM2014v205n12ABEH004439
Abstract: Conditions are obtained for the image of a given set under a general completely continuous nonlinear integral operator to have convex closure. These results are used to establish the uniqueness of quasi-solutions of nonlinear integral equations of the first kind and to prove the solvability of equations of the first kind on a dense subset of the right-hand sides.
Bibliography: 11 titles.
Keywords: nonlinear integral operator, image of a set, closure, convexity, equation of the first kind.
Funding agency Grant number
Russian Foundation for Basic Research 12-01-00239a
Received: 19.05.2014 and 07.09.2014
Russian version:
Matematicheskii Sbornik, 2014, Volume 205, Number 12, Pages 99–110
DOI: https://doi.org/10.4213/sm8386
Bibliographic databases:
Document Type: Article
UDC: 517.988
MSC: Primary 47H30, 45G10, 45N05; Secondary 46N20, 47H04
Language: English
Original paper language: Russian
Citation: M. Yu. Kokurin, “Convexity properties of images under nonlinear integral operators”, Mat. Sb., 205:12 (2014), 99–110; Sb. Math., 205:12 (2014), 1775–1786
Citation in format AMSBIB
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  • https://doi.org/10.1070/SM2014v205n12ABEH004439
  • https://www.mathnet.ru/eng/sm/v205/i12/p99
    • This publication is cited in the following 3 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Abstract page:461
    Russian version PDF:170
    English version PDF:14
    References:54
    First page:31
     
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