On the Sendov problem on the Whitney interpolation constant

• Date: 1998
• Main Authors: Danilenko, I. G., Даниленко, І. Г.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 1998
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4911
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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...