单纯型上广义Bernstein算子  

Generalized Bernstein Operators Defined on a Simplex

作　　者：丁春梅[1] 杨汝月[1] 

机构地区：[1]中国计量学院信息与数学科学系,杭州310018

出　　处：《数学物理学报（A辑）》2009年第2期423-435,共13页Acta Mathematica Scientia

基　　金：国家自然科学基金(90818020;60873206);浙江省自然科学基金(Y7080235);浙江省教育厅科研重点项目基金(20060543)资助

摘　　要：该文引进并研究定义在n维单纯型上的广义Bernstein算子.首先,证明该算子具有对称性和保持Lipshcitz性质.其次,借助多元Ditzian-Totik连续模,得到该算子逼近连续函数的一个强型正向估计和一个弱型逆向不等式.最后,给出参数s_n满足不同条件的若干Voronovskaja型展开式.该文所获得的结果包含了经典的Bernstein算子的相应结果.In this paper, the authors introduce and study generalized Bernstein operators defined on a simplex in R. They first prove that these operators possess the symmetric property for a transformation from the simplex to itself and the Lipshcitz property. Then, by means of the multivariate Ditzian-Totik＇s modulus of continuity, they obtain a strong type direct estimate and an inverse inequality of weak type for the operators approximating multivariate continuous functions. Finally, they give some Voronovskaja type expansions when the parameters sn satisfy some conditions. The obtained results include the corresponding ones of the classical Bernstein operators as a corollary.

关 键 词：广义Bernstein算子 连续模 正定理 逆定理 Voronovskaja型展开. 

分 类 号：O174.41[理学—数学]