Estimate of the Remainder of the Best Quadratic Approximation of Differentiable Functions by Polynomials
Abstract
We establish lower and upper bounds for the quantity Cqm(Wr,x)=supf∈Wr|f(x)−Tm(x,f)|, , where Tm(x,f)=2qq−1∑l=0f(xl)Dm(x−xl),q∈N,q>2m,xl=2πlq,l=0,1,...,q−1, , 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.Downloads
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.