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Russian Universities Reports. Mathematics, 2021, Volume 26, Issue 133, Pages 44–54 (Mi vtamu215)  

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

Scientific articles

On stability of solutions of integral equationsin the class of measurable functions

W. Merchela

University May 8, 1945 – Guelma
Full-text PDF (604 kB) Citations (2)
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Abstract: Consider the equation $G(x)=\tilde{y},$ where the mapping $G$ acts from a metric space $X$ into a space $Y,$ on which a distance is defined, $\tilde{y} \in Y.$ The metric in $X$ and the distance in $Y$ can take on the value $\infty,$ the distance satisfies only one property of a metric: the distance between $y, z \in Y$ is zero if and only if $y=z.$ For mappings $X \to Y$ the notions of sets of covering, Lipschitz property, and closedness are defined. In these terms, the assertion is obtained about the stability in the metric space $X$ of solutions of the considered equation to changes of the mapping $G$ and the element $\tilde{y}.$ This assertion is applied to the study of the integral equation
$$ f \big(t, \int_0^1 \mathcal{K}(t,s)x(s) ds, x(t)\big)=\tilde{y}(t), \ \ t \in [0.1], $$
with respect to an unknown Lebesgue measurable function $x: [0,1] \to \mathbb {R}.$ Sufficient conditions are obtained for the stability of solutions (in the space of measurable functions with the topology of uniform convergence) to changes of the functions $f, \mathcal{K}, \tilde{y}.$
Keywords: operator equation; existence of solutions; stability of solutions; covering mapping; distance; space of measurable functions; integral equation.
Document Type: Article
UDC: 517.988.63+517.968.4+515.124.4
Language: Russian
Citation: W. Merchela, “On stability of solutions of integral equationsin the class of measurable functions”, Russian Universities Reports. Mathematics, 26:133 (2021), 44–54
Citation in format AMSBIB
\Bibitem{Mer21}
\by W.~Merchela
\paper On stability of solutions of integral equations\\ in the class of measurable functions
\jour Russian Universities Reports. Mathematics
\yr 2021
\vol 26
\issue 133
\pages 44--54
\mathnet{http://mi.mathnet.ru/vtamu215}
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  • https://www.mathnet.ru/eng/vtamu/v26/i133/p44
  • This publication is cited in the following 2 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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    Russian Universities Reports. Mathematics
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