Exact constant in the Dzyadyk inequality for the derivative of an algebraic polynomial
Abstract
For natural k and n≥2k, we determine the exact constant c(n,k) in the Dzyadyk inequality ||P′nφ1−kn||C[1,1]≤c(n,k)n‖ for the derivative P^{\prime}_n of an algebraic polynomial P_n of degree \leq n, where \varphi_n(x) := \sqrt{n^{-2} + 1 - x_2,} . Namely, c(n, k) = \biggl( 1 + k \frac{\sqrt{ 1 + n^2} - 1}{n} \biggr)^2 - k.Downloads
Published
25.05.2017
Issue
Section
Research articles
How to Cite
Galan, V. D., and I. A. Shevchuk. “Exact Constant in the Dzyadyk Inequality for the Derivative of an Algebraic Polynomial”. Ukrains’kyi Matematychnyi Zhurnal, vol. 69, no. 5, May 2017, pp. 624-30, https://umj.imath.kiev.ua/index.php/umj/article/view/1721.