Approximation of a convex function by convex algebraic polynomials in \(L_ p,1{\leq}p<\infty\)
type: Item
instance of: scholarly article
title: Approximation of a convex function by convex algebraic polynomials in \(L_ p,1{\leq}p<\infty\)
zbMATH Open document ID: 0788.41005
author: M. Nikoltjeva-Hedberg
published in: Journal of Approximation Theory
publication date: 1994-05-19T00:00:00Z
review text: The paper deals with the best approximation of a convex function by convex algebraic polynomials in \(L_ p\), \(1\leq p<\infty\). Pending a number of lemmas it is proved: Let \(f\) be a convex function on \([-1,1]\) such that \(\max_{x\in[-1,1]} f(x)=1\), \(\min_{x\in [-1,1]} f(x)=0\). Then for every \(n\) there exists a convex polynomial \(Q_ n\) of degree at most \(n\) such that \(\| f-Q_ n\|_ p\leq An^{-2/p}\), \(1\leq p<\infty\), where \(A\) is a constant independent of \(f\) and \(p\).
Mathematics Subject Classification ID: 41A10
Mathematics Subject Classification ID: 41A25
zbMATH DE Number: 205441
zbMATH Keywords: convex algebraic polynomials
reviewed by: Margareta Heilmann
MaRDI profile type: Publication
full work available at URL: jath.1993.1043
OpenAlex ID: W2090738536
DOI: 10.1006/JATH.1993.1043
description: scientific article; zbMATH DE number 205441