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On the Sendov problem on the Whitney interpolation constant

For a function ƒ continuous on [0, 1] and satisfying the equalities \(f(0) = f\left( {\frac{1}{3}} \right) = f\left( {\frac{2}{3}} \right) = f(1) = 0,\) we prove that \(|f(x)| \le 2\omega _4 \left( {\frac{1}{4},f} \right),{\rm{ }}x \in [0,1],\) where ω4(t,ƒ) is the fourth modulus of smoothne...

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Datum:1998
Hauptverfasser: Danilenko, I. G., Даниленко, І. Г.
Format: Artikel
Sprache:Ukrainisch
Englisch
Veröffentlicht: Institute of Mathematics, NAS of Ukraine 1998
Online Zugang:https://umj.imath.kiev.ua/index.php/umj/article/view/4911
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Назва журналу:Ukrains’kyi Matematychnyi Zhurnal
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Ukrains’kyi Matematychnyi Zhurnal
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author Danilenko, I. G.
Даниленко, І. Г.
author_facet Danilenko, I. G.
Даниленко, І. Г.
author_sort Danilenko, I. G.
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datestamp_date 2020-03-18T21:16:53Z
description For a function ƒ continuous on [0, 1] and satisfying the equalities \(f(0) = f\left( {\frac{1}{3}} \right) = f\left( {\frac{2}{3}} \right) = f(1) = 0,\) we prove that \(|f(x)| \le 2\omega _4 \left( {\frac{1}{4},f} \right),{\rm{ }}x \in [0,1],\) where ω4(t,ƒ) is the fourth modulus of smoothness of the function ƒ.
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spelling umjimathkievua-article-49112020-03-18T21:16:53Z On the Sendov problem on the Whitney interpolation constant До проблеми Сендова про інтерполяційну сталу Уітні Danilenko, I. G. Даниленко, І. Г. For a function ƒ continuous on [0, 1] and satisfying the equalities \(f(0) = f\left( {\frac{1}{3}} \right) = f\left( {\frac{2}{3}} \right) = f(1) = 0,\) we prove that \(|f(x)| \le 2\omega _4 \left( {\frac{1}{4},f} \right),{\rm{ }}x \in [0,1],\) where ω4(t,ƒ) is the fourth modulus of smoothness of the function ƒ. Для неперервної на [0,1] функції $ƒ$, що задовольняє рівності $f(0) = f\left( {\frac{1}{3}} \right) = f\left( {\frac{2}{3}} \right) = f(1) = 0,$ доведено, що $|f(x)| \le 2\omega _4 \left( {\frac{1}{4},f} \right),{\rm{ }}x \in [0,1],$, де $ω_4(t,ƒ)$ — четвертий модуль гладкості функції $ƒ$. Institute of Mathematics, NAS of Ukraine 1998-05-25 Article Article application/pdf https://umj.imath.kiev.ua/index.php/umj/article/view/4911 Ukrains’kyi Matematychnyi Zhurnal; Vol. 50 No. 5 (1998); 732–734 Український математичний журнал; Том 50 № 5 (1998); 732–734 1027-3190 uk en https://umj.imath.kiev.ua/index.php/umj/article/view/4911/6521 https://umj.imath.kiev.ua/index.php/umj/article/view/4911/6522 Copyright (c) 1998 Danilenko I. G.
spellingShingle Danilenko, I. G.
Даниленко, І. Г.
On the Sendov problem on the Whitney interpolation constant
title On the Sendov problem on the Whitney interpolation constant
title_alt До проблеми Сендова про інтерполяційну сталу Уітні
title_full On the Sendov problem on the Whitney interpolation constant
title_fullStr On the Sendov problem on the Whitney interpolation constant
title_full_unstemmed On the Sendov problem on the Whitney interpolation constant
title_short On the Sendov problem on the Whitney interpolation constant
title_sort on the sendov problem on the whitney interpolation constant
url https://umj.imath.kiev.ua/index.php/umj/article/view/4911
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