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Matematicheskie Zametki, 2022, Volume 111, Issue 1, paper published in the English version journal
(Mi mzm13398)
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This article is cited in 4 scientific papers (total in 4 papers)
Papers published in the English version of the journal
Continuity of $L_{p}$ Balls and an Application
to Input-Output Systems
A. Huseyina, N. Huseyinb, Kh. G. Guseinovc a Department of Statistics and Computer Sciences, Sivas
Cumhuriyet University, Sivas, 58140 Turkey
b Department of Mathematics and Science Education, Sivas
Cumhuriyet University, Sivas, 58140 Turkey
c Department of Mathematics, Eskisehir Technical
University, Eskisehir, 26470 Turkey
Abstract:
In this paper, the continuity of the set-valued map
$p\rightarrow
B_{\Omega,\mathcal{X},p}(r)$,
$p\in (1,+\infty)$,
is proved where
$B_{\Omega,\mathcal{X},p}(r)$
is the closed ball of radius $r$ in the space
$L_{p}(\Omega,\Sigma,\mu;
\mathcal{X})$
centered at the origin,
$(\Omega,\Sigma,\mu)$
is a finite
and positive measure space, and
$\mathcal{X}$
is a separable Banach space.
An application to
input-output systems described by Urysohn type integral operators is discussed.
Keywords:
continuity, Hausdorff distance, set-valued map, input-output system, integrable output.
Received: 01.06.2021 Revised: 17.07.2021
Citation:
A. Huseyin, N. Huseyin, Kh. G. Guseinov, “Continuity of $L_{p}$ Balls and an Application
to Input-Output Systems”, Math. Notes, 111:1 (2022), 58–70
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https://www.mathnet.ru/eng/mzm13398
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