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arXiv · 1705.05614

On the Jackson constants for algebraic approximation of continuous functions

A. G. Babenko·Yu. V. Kryakin
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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: $$ E_{n}^a (f) \le J_a(k, α) \ ω_k (f, απ/n ), \quad α>0 $$ The main result of the paper implies the following inequalities $$ 1/2< J_a (2k, α) < 10, \quad n \ge 2k(2k-1), \quad α\ge 2 $$

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A. G. Babenko, Yu. V. Kryakin. 2017-05-16. On the Jackson constants for algebraic approximation of continuous functions. https://arxiv.org/abs/1705.05614

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