On the Jackson constants for algebraic approximation of continuous functions

2017/05/16 by А. Г. Бабенко, Babenko, A. G., Yu. V. Kryakin +1
Mathematics · Computer Science · #Approximation Theory and Sequence Spaces #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1705.05614

Abstract

We establish new estimates for the constant J_a(k,α) in the Brudnyi-Jackson inequality for approximation of f ∈ C[-1,1] by algebraic polynomials: E_n^a (f) ≤ J_a(k, α) ω_k (f, απ/n ), αgt;0 The main result of the paper implies the following inequalities 1/2lt; J_a (2k, α) lt; 10, n ≥ 2k(2k-1), α≥ 2

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