| 一类多元三角多项式算子同时逼近的正逆定理 |
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| 引用本文： | 魏淑清.一类多元三角多项式算子同时逼近的正逆定理[J].宁夏大学学报(自然科学版),2007,28(4):301-304. |
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| 作者姓名： | 魏淑清 |
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| 作者单位： | 北方民族大学,商学院,宁夏,银川,750021 |
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| 摘 要： | 利用光滑模和K-泛函给出了一类多元三角多项式算子同时逼近的正逆定理．进一步得出了该类算子的本质同时逼近精度和最大同时逼近能力，刻画了同时逼近精度与被逼近函数光滑性之间的关系．
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| 关 键 词： | 三角多项式算子 同时逼近 光滑模 K-泛函 |
| 文章编号： | 0253-2328（2007）04-0301-04 |
| 收稿时间： | 2006-08-28 |
| 修稿时间： | 2006年8月28日 |
Direct and Inverse Theorems of Simultaneous Approximation for A Kind of Multivariate Trigonometric Polynomial Operators |
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| Wei Shuqing.Direct and Inverse Theorems of Simultaneous Approximation for A Kind of Multivariate Trigonometric Polynomial Operators[J].Journal of Ningxia University(Natural Science Edition),2007,28(4):301-304. |
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| Authors: | Wei Shuqing |
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| Abstract: | Using the modulus of smoothness and K-functional, direct and inverse theorems of simultaneous approximation for a kind of multivariate trigonometric polynomial operators are established. Its accuracy and maximal ability of simultaneous approximation is obtained, and the relation between accuracy and the smoothness of function to be approximated is depicted. |
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| Keywords: | trigonometric polynomial operator simultaneous approximation modulus of smoothness K-functional |
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