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Matematicheskie Zametki, 2016, Volume 100, Issue 4, Pages 544–552
DOI: https://doi.org/10.4213/mzm10687
(Mi mzm10687)
 

This article is cited in 2 scientific papers (total in 2 papers)

On the Convexity of Images of Nonlinear Integral Operators

M. Yu. Kokurin

Mari State University, Ioshkar-Ola
Full-text PDF (483 kB) Citations (2)
References:
Abstract: We study continuous nonlinear Urysohn-type integral operators acting from the spaces of vector functions with integrable components to the space of continuous functions. We obtain conditions under which the images of sets defined by pointwise constraints have a convex closure under the action of these operators. The result is used to justify a method of constructive approximation of these images and to derive a necessary solvability condition for Urysohn-type integral equations. A numerical method for finding the residual of equations of this type on the sets under consideration is justified.
Keywords: nonlinear integral operator, multivalued mapping, image of a set, closure, convexity, quasisolution.
Funding agency Grant number
Russian Foundation for Basic Research 15-07-99514a
16-01-00039a
This work was supported by the Russian Foundation for Basic Research under grants no. 15-07-99514a and no. 16-01-00039a.
Received: 27.03.2015
English version:
Mathematical Notes, 2016, Volume 100, Issue 4, Pages 561–567
DOI: https://doi.org/10.1134/S0001434616090273
Bibliographic databases:
Document Type: Article
Language: Russian
Citation: M. Yu. Kokurin, “On the Convexity of Images of Nonlinear Integral Operators”, Mat. Zametki, 100:4 (2016), 544–552; Math. Notes, 100:4 (2016), 561–567
Citation in format AMSBIB
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  • https://doi.org/10.4213/mzm10687
  • https://www.mathnet.ru/eng/mzm/v100/i4/p544
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
    Related articles in Google Scholar: Russian articles, English articles
    Математические заметки Mathematical Notes
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    References:37
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