On the Sendov problem on the Whitney interpolation constant

  • I. G. Danilenko

Abstract

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.
Published
25.05.1998
How to Cite
DanilenkoI. G. “On the Sendov Problem on the Whitney Interpolation Constant”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 50, no. 5, May 1998, pp. 732–734, https://umj.imath.kiev.ua/index.php/umj/article/view/4911.
Section
Short communications