Estimate of the Remainder of the Best Quadratic Approximation of Differentiable Functions by Polynomials

• Date: 2004
• Main Authors: Grigoryan, A. L., Григорян, А.Л.
• Format: Article
• Language: Russian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3876
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We establish lower and upper bounds for the quantity $$C_m^q (W^r ,x) = \mathop {\sup }\limits_{f \in W^r } \left| {f(x) - T_m (x,f)} \right|,$$ , where $$T_m (x,f) = \frac{2}{q}\mathop \sum \limits_{l = 0}^{q - 1} \;f(x_l )D_m (x - x_l ),\quad q \in \mathbb{N},\quad q > 2m,\quad x_l = \...