On the Jackson constants for algebraic approximation of continuous functions

A. G. Babenko; Yu. V. Kryakin

paper

On the Jackson constants for algebraic approximation of continuous functions

arXiv:1705.05614

Abstract

We establish new estimates for the constant $J_{a} (k, α)$ in the Brudnyi-Jackson inequality for approximation of $f \in C [- 1, 1]$ by algebraic polynomials: $E_{n}^{a} (f) \leq J_{a} (k, α) ω_{k} (f, α π / n), α > 0$ The main result of the paper implies the following inequalities $1/2 < J_{a} (2 k, α) < 10, n \geq 2 k (2 k - 1), α \geq 2$