Coconvex Approximation of Functions with More than One Inflection Point

• Date: 2004
• Main Authors: Dzyubenko, H. A., Zalizko, V. D., Дзюбенко, Г. А., Залізко, В. Д.
• Format: Article
• Language: Ukrainian; English
• Published: Institute of Mathematics, NAS of Ukraine 2004
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/3759
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Assume that f ∈ C[−1, 1] belongs to C[−1, 1] and changes its convexity at s > 1 different points y i, \(\overline {1,s} \) , from (−1, 1). For n ∈ N, n ≥ 2, we construct an algebraic polynomial P n of order ≤ n that changes its convexity at the same points y i as f and is such that $$|f(...