Strong type of Steckin inequality for the linear combination of Bernstein operators

JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS

卷:408

Article

Xie, Linsen

关键词: Bernstein operator;    Combination;    Strong type of Steckin inequality;    Modulus of smoothness;   

DOI  :  10.1016/j.jmaa.2013.06.007

来源: Elsevier

【 摘 要 】

In this paper we obtain a new strong type of Steckin inequality for the linear combinations of Bernstein operators, which gives the optimal approximation rate. Moreover, a method to prove lower estimates for linear operators is introduced. As a result the lower estimate for the linear combinations of Bernstein operators is obtained by using the Ditzian-Totik modulus of smoothness. (C) 2013 Published by Elsevier Inc.

【 授权许可】

Free