Coconvex Pointwise Approximation

• Date: 2002
• Main Authors: Dzyubenko, H. A., Gilewicz, J., Shevchuk, I. A., Дзюбенко, Г. А., Гілевич, Я. Я., Шевчук, І. О.
• Format: Article
• Language: English
• Published: Institute of Mathematics, NAS of Ukraine 2002
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/4159
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

Assume that a function f ∈ C[−1, 1] changes its convexity at a finite collection Y := {y 1, ... y s} of s points y i ∈ (−1, 1). For each n > N(Y), we construct an algebraic polynomial P n of degree ≤ n that is coconvex with f, i.e., it changes its convexity at the same points y i as f and $...