修正Bernstein算子的导数及其加权光滑性刻画  

Derivatives of Modified Bernstein Operators and Smoothness with Jacobi Weights

作　　者：王美玲[1] 

机构地区：[1]杭州师范大学理学院,浙江杭州310036

出　　处：《浙江外国语学院学报》2014年第5期44-48,55,共6页Journal of Zhejiang International Studies University

摘　　要：Della Vecchia等引进一种修正的Bernstein算子,它可以用来逼近端点具有奇性的函数。文章利用加权光滑模ω2φλ(f,t)w和加权K-泛函K2φλ(f,t2)w,建立了该算子的导数与其目标函数的光滑性之间的等价关系,所得结论对权函数的参数a,b无上界限制,只要求a,b>0。In the present paper,we establish the equivalent relation between the derivatives of a modified Bernstein operators and the smoothness of the functions which approximate in the weighted approximation,by using the weighted modulus of smoothness and the weighted K-functional.All the results involved have no re-striction on the upper bounds of the parameters a and b.

关 键 词：奇性函数 加权逼近 BERNSTEIN算子 等价关系 

分 类 号：O174.41[理学—数学]