Coconvex Pointwise Approximation

• Published in: Український математичний журнал
• Date: 2002
• Main Authors: Dzyubenko, G.A., Gilewicz, J., Shevchuk, I.A.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2002
• Subjects: Статті
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/164317
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Coconvex Pointwise Approximation / G.A. Dzyubenko, J.Gilewicz, I.A. Shevchuk // Український математичний журнал. — 2002. — Т. 54, № 9. — С. 1200–1212. — Бібліогр.: 17 назв. — англ.

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