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

[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.

[发布日期] 2013-12-15

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