Coconvex Approximation of Functions with More than One Inflection Point
Abstract
Assume that f ∈ C[−1, 1] belongs to C[−1, 1] and changes its convexity at s > 1 different points y i, ¯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(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.Downloads
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.