Are the degrees of the best (co)convex and unconstrained polynomial approximations the same? II

• Date: 2010
• Main Authors: Kopotun, K. A., Leviatan, D., Shevchuk, I. A., Коротун, К. А., Левіатан, Д., Шевчук, І. О.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2010
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/2873
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

In Part I of the paper, we have proved that, for every $α > 0$ and a continuous function $f$, which is either convex $(s = 0)$ or changes convexity at a finite collection $Y_s = \{y_i\}^s_i = 1$ of points $y_i ∈ (-1, 1)$, $$\sup \left\{n^{\alpha}E^{(2)}_n(f,Y_s):\;n \geq N^{*}\right\} \leq c(...