| 第二类Beta算子对一类导数有界函数的逼近 |
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| 引用本文： | 蔡清波,王平华. 第二类Beta算子对一类导数有界函数的逼近[J]. 泉州师范学院学报, 2008, 26(6): 1-4 |
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| 作者姓名： | 蔡清波 王平华 |
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| 作者单位： | 泉州师范学院理工学院,福建,泉州,362000 |
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| 基金项目： | 国家自然科学基金项目，福建省自然科学基金资助项目 |
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| 摘 要： | 研究了第二类Beta算子的逼近性质，通过直接计算得到第二类Beta算子Ln（t-x｜，z）的一阶绝对矩的最优估计，由此估计结果结合Bojanic-Cheng-Khan的方法以及分析技巧，导出第二类Beta算子对一类导数有界函数的渐近估计，得出该算子的一个渐近展开公式．
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| 关 键 词： | 绝对连续函数 Beta型算子 收敛阶 Lebesgue-Stieltjes积分 矩 |
Rate of Convergence of Beta Operators of Second Kind for a Class of Bounded Functions with Derivatives |
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| CAI Qin-gbo,WANG Ping-hua. Rate of Convergence of Beta Operators of Second Kind for a Class of Bounded Functions with Derivatives[J]. Journal of Quanzhou Normal College, 2008, 26(6): 1-4 |
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| Authors: | CAI Qin-gbo WANG Ping-hua |
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| Affiliation: | (School of Science, Quanzhou Normal University, Fujian 362000, China) |
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| Abstract: | This paper studies the approximation properties of Beta operators of second kind.The optimal estimate on the first order absolute moment of Beta type operators Ln of second kind Ln(|t-x|,x) is obtained by direct computations.And then this estimate and Bojanic-Cheng-Khan's method combining with analytical techniques are used to derive an asymptotically optimal estimation on the rate of convergence of Beta type operators Ln of second kind for a class of bounded functions with derivatives. |
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| Keywords: | absolutely continuous functions Beta type operators rate of convergence Lebesgue-Stieltjes integral moments |
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