Vallée-Poussin算子逼近连续函数的最优估计  

The Optimal Estimation of Vallée-Poussin Operator Approximating to Continuous Functions

作　　者：董灏[1] 聂玉峰[1] 崔俊芝[2] 

机构地区：[1]西北工业大学理学院应用数学系,陕西西安710129 [2]中国科学院数学与系统科学研究院计算数学与科学工程计算研究所,北京100190

出　　处：《数学的实践与认识》2017年第3期214-217,共4页Mathematics in Practice and Theory

基　　金：陕西高等教育教学改革研究项目(13BY12)

摘　　要：通过将Vallée-Poussin算子逼近连续函数的能力转化为对辅助数列{g(n)}的上确界的计算,首先利用数列单调有界定理证明辅助数列极限的存在性,之后借助夹逼准则求得辅助数列{g(n)}的极限,即数列{g(n)}的上确界,进而得到Vallée-Poussin算子逼近连续函数的最优估计常数.In this paper, the capacity of Vallee-Poussin operators approximation of continuous func- tions was transformed into the calculation of the supremum of the auxiliary series. Firstly the existent limit of auxiliary sequence was proved by series monotone bound theorem, and then the limitation of auxiliary series was obtained by Squeeze rule, which is the supremum of series. Finally the optimal estimation constant of Vallee-Poussin operators approximation of continuous functions was found.

关 键 词：单调有界定理 夹逼准则 上确界 数列极限 最优估计 

分 类 号：O177[理学—数学] O174.41[理学—基础数学]