Bernstein算子2r阶导数与光滑模的等价关系  

An Equivalent Relation Between the Derivatives ofOrder 2r of Bernstein Operators andthe Modulus of Smoothness

作　　者：冯国[1] 

机构地区：[1]台州学院数学系,浙江临海317000

出　　处：《山西大学学报（自然科学版）》2002年第3期202-205,共4页Journal of Shanxi University(Natural Science Edition)

基　　金：浙江省自然科学基金 (1980 36 )

摘　　要：利用 Ditzian- Totik光滑模 ω2 rλ(f,t) (0≤ λ≤ 1)研究了 Bernstein算子 2 r阶导数与它所逼近的函数的光滑性之间的关系 ,得到 Bernstein算子 2 r阶导数与 Ditzian- Totik光滑模关系的等价定理。统一了 Bernstein算子 2The relationship between the derivatives of order 2r of the Bernstein operators and the smoothness of the function Bernstein operators approximates was studied by using the Ditzian-Totik modulusω\+\{2r\}\-\{\+λ\}(f,t)(0≤λ≤1),and was got the equivalent theorem between the derivatives of Bernstein operators and the Ditzian-Totik modulus.These results bridge the gap between the pointwise and global conclusions.

关 键 词：BERNSTEIN算子 2r阶导数 等价关系 DITZIAN-TOTIK光滑模 等价定理 函数逼近 算子逼近 

分 类 号：O174.41[理学—数学]