Exact constant in the Dzyadyk inequality for the derivative of an algebraic polynomial

Authors

  • V. D. Galan
  • I. A. Shevchuk

Abstract

For natural k and n2k, we determine the exact constant c(n,k) in the Dzyadyk inequality ||Pnφ1kn||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.

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.