Estimate of the Remainder of the Best Quadratic Approximation of Differentiable Functions by Polynomials

Authors

  • A. L. Grigoryan

Abstract

We establish lower and upper bounds for the quantity Cqm(Wr,x)=supfWr|f(x)Tm(x,f)|, , where Tm(x,f)=2qq1l=0f(xl)Dm(xxl),qN,q>2m,xl=2πlq,l=0,1,...,q1, , and D m (t) is the Dirichlet kernel, for the class W r of 2π-periodic functions, whose rth derivative satisfies the condition |f r (x)| ≤ 1.

Published

25.12.2004

Issue

Section

Short communications

How to Cite

Grigoryan, A. L. “Estimate of the Remainder of the Best Quadratic Approximation of Differentiable Functions by Polynomials”. Ukrains’kyi Matematychnyi Zhurnal, vol. 56, no. 12, Dec. 2004, pp. 1691-8, https://umj.imath.kiev.ua/index.php/umj/article/view/3876.