Bernstein型算子在Wiener空间逼近的平均误差  

Average errors for Bernstein type operator approximation on Wiener space

作　　者：包淑华[1,2] 

机构地区：[1]华北电力大学数理学院,河北保定071003 [2]呼伦贝尔学院数学与统计学院,内蒙古呼伦贝尔021008

出　　处：《天津师范大学学报（自然科学版）》2016年第2期15-18,共4页Journal of Tianjin Normal University：Natural Science Edition

基　　金：内蒙古自治区自然科学基金资助项目(2015BS0103)

摘　　要：利用多个相邻点函数值的平均值代替单点函数值构造Bernstein型算子.利用Wiener空间的基本性质,借助一些常用不等式及多变量分块求和的技巧,得到了该算子在Wiener空间上逼近的误差估计.结果表明,该算子在上述测度空间上的平均逼近误差与经典Bernstein算子相应的平均逼近误差是同阶的.By using average value of multi neighboring points function values instead of the single value,a Bernstein type operator is constructed. By combining with the basic property of Wiener space,some common inequalities and skills of multi-variable block summation,the error estimate of approximation for this operator is obtained on the Wiener space. The conclu-sion shows that the average approximation errors are in the same order with the classic Bernstein operator on the measuring space.

关 键 词：BERNSTEIN型算子 WIENER空间 平均误差 

分 类 号：O172.42[理学—数学]