The complete asymptotic expansion for Bernstein operators

被引：25
|
作者：
Tachev, Gancho T. [1 ]
机构：
[1] Univ Architecture, Dept Math, BG-1046 Sofia, Bulgaria
来源：
JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS | 2012年 / 385卷 / 02期
关键词：
Bernstein operator; Positive linear operators; Moduli of continuity (smoothness); Degree of approximation; APPROXIMATION;
D O I：
10.1016/j.jmaa.2011.07.042
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we study the asymptotic behavior of the classical Bernstein operators, applied to q-times continuously differentiable functions. Our main results extend the results of S.N. Bernstein and R.G. Mamedov for all q-odd natural numbers and thus generalize the theorem of E.V. Voronovskaja. The exact degree of approximation is also proved. (C) 2011 Elsevier Inc. All rights reserved.
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页码：1179 / 1183
页数：5
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