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On the Jackson constants for algebraic approximation of continuous functions. (arXiv:1705.05614v1 [math.CA])
来源于:arXiv
We establish new estimates for the constant $J_a(k,\alpha)$ in the
Brudnyi-Jackson inequality for approximation of $f \in C[-1,1]$ by algebraic
polynomials:
$$ E_{n}^a (f) \le J_a(k, \alpha) \ \omega_k (f, \alpha \pi /n ), \quad
\alpha >0 $$
The main result of the paper implies the following inequalities
$$ 1/2< J_a (2k, \alpha) < 10, \quad n \ge 2k(2k-1), \quad
\alpha \ge 2 $$ 查看全文>>
