Coconvex Approximation of Functions with More than One Inflection Point

Authors

  • H. A. Dzyubenko
  • V. D. Zalizko

Abstract

Assume that fC[−1, 1] belongs to C[−1, 1] and changes its convexity at s > 1 different points y i, ¯1,s , from (−1, 1). For nN, 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(x)Pn(x)| where ω3(f; t) is the third modulus of continuity of the function f and C(Y) is a constant that depends only on \mathop {\min }\limits_{i = 0,...,s} \left| {y_i - y_{i + 1} } \right|,\;\;y_0 = 1,\;\;y_{s + 1} = - 1 , y 0 = 1, y s + 1 = −1.

Published

25.03.2004

Issue

Section

Research articles

How to Cite

Dzyubenko, H. A., and V. D. Zalizko. “Coconvex Approximation of Functions With More Than One Inflection Point”. Ukrains’kyi Matematychnyi Zhurnal, vol. 56, no. 3, Mar. 2004, pp. 352-65, https://umj.imath.kiev.ua/index.php/umj/article/view/3759.