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Funktsional'nyi Analiz i ego Prilozheniya, 2022, Volume 56, Issue 4, Pages 43–58
DOI: https://doi.org/10.4213/faa3974 (Mi faa3974) 		 
This article is cited in 2 scientific papers (total in 2 papers)

Approximations of the Images and Integral Funnels of the $L_p$ Balls under a Urysohn-Type Integral Operator

A. Huseyina, N. Huseyinb, Kh. G. Guseinovc

a Cumhuriyet University, Faculty of Science, Department of Statistics and Computer Sciences
b Cumhuriyet University, Faculty of Education, Department of Mathematics and Science Education
c Eskisehir Technical University, Faculty of Science, Department of Mathematics
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DOI: https://doi.org/10.4213/faa3974
Abstract: Approximations of the image and integral funnel of a closed ball of the space $L_p$, $p>1$, under a Urysohn-type integral operator are considered. A closed ball of the space $L_p$, $p>1$, is replaced by a set consisting of a finite number of piecewise constant functions, and it is proved that, for appropriate discretization parameters, the images of these piecewise constant functions form an internal approximation of the image of the closed ball. This result is applied to approximate the integral funnel of a closed ball of the space $L_p$, $p>1$, under a Urysohn-type integral operator by a set consisting of a finite number of points.
Keywords: Urysohn integral operator, image of $L_p$ ball, integral funnel, approximation, input-output system.
Received: 26.12.2021
Revised: 02.06.2022
Accepted: 10.06.2022
English version:
Functional Analysis and Its Applications, 2022, Volume 56, Issue 4, Pages 269–281
DOI: https://doi.org/10.1134/S0016266322040050
Bibliographic databases:
Document Type: Article
UDC: 517.98
Language: Russian
Citation: A. Huseyin, N. Huseyin, Kh. G. Guseinov, “Approximations of the Images and Integral Funnels of the $L_p$ Balls under a Urysohn-Type Integral Operator”, Funktsional. Anal. i Prilozhen., 56:4 (2022), 43–58; Funct. Anal. Appl., 56:4 (2022), 269–281
Citation in format AMSBIB
\Bibitem{HusHusGus22}
\by A.~Huseyin, N.~Huseyin, Kh.~G.~Guseinov
\paper Approximations of the Images and Integral Funnels of the $L_p$ Balls under a Urysohn-Type Integral Operator
\jour Funktsional. Anal. i Prilozhen.
\yr 2022
\vol 56
\issue 4
\pages 43--58
\mathnet{http://mi.mathnet.ru/faa3974}
\crossref{https://doi.org/10.4213/faa3974}
\transl
\jour Funct. Anal. Appl.
\yr 2022
\vol 56
\issue 4
\pages 269--281
\crossref{https://doi.org/10.1134/S0016266322040050}
\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-85142366967}
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  • https://www.mathnet.ru/eng/faa/v56/i4/p43
    • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    		Функциональный анализ и его приложения Functional Analysis and Its Applications
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