The Whitney constants are bounded by two
type: Item
instance of: scholarly article
title: The Whitney constants are bounded by two
zbMATH Open document ID: 0809.41010
DOI: 10.1007/BF01208555
author: Yu. V. Kryakin
published in: Mathematical Notes
publication date: 1994-07-13T00:00:00Z
review text: The following refinement of Whitney's classical result is proved: for any \(f \in C[0;1]\) and an algebraic polynomial of degree at most \((n-1)\) such that \(\int^{i/n}_ 0 (f(t) - P(t))dt = 0\), \(i=1, \dots, n\), the inequality \(\| f - P \|_{C[0;1]} \leq 2 \omega_ n (t)\) hold. (Here \(\omega_ n (f)\) is the \(n\)-th modulo of smoothness for \(f)\).
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A44
zbMATH DE Number: 589625
zbMATH Keywords: Whitney's inequality
zbMATH Keywords: algebraic polynomial
zbMATH Keywords: modulo of smoothness
reviewed by: Alexei Lukashov
MaRDI profile type: Publication
cites work: Q4749793
full work available at URL: https://doi.org/10.1007/bf01208555
OpenAlex ID: W2090348549
description: scientific article; zbMATH DE number 589625