The complete asymptotic expansion for Bernstein operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:385

Article

Tachev, Gancho T.

关键词: Bernstein operator;    Positive linear operators;    Moduli of continuity (smoothness);    Degree of approximation;   

DOI  :  10.1016/j.jmaa.2011.07.042

来源: Elsevier

【 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.

【 授权许可】

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