| Bernstein算子的强逆不等式 |
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| 引用本文： | 郭顺生,齐秋兰. Bernstein算子的强逆不等式[J]. 数学学报, 2003, 46(5): 891-896. DOI: cnki:ISSN:0583-1431.0.2003-05-007 |
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| 作者姓名： | 郭顺生 齐秋兰 |
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| 作者单位： | 河北师范大学数学与信息科学学院,石家庄,050016 |
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| 基金项目： | 河北省自然科学基金(101090)，河北师范大学重点学科基金，博士基金资助项目 |
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| 摘 要： | 本文对Bernstein算子证明了其强逆不等式,这些不等式曾被Ditzian,Ivanov,Totik,李松等人用不同的方法得到过,但其结果是通常的估计(λ=1),古典的结果(λ=0)没有包含,本文引入κ-泛函K_λ~α(f,t~2)(0≤λ≤1,0<α<2),将已有结果推广到0≤λ≤1的情形。
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| 关 键 词： | Bernstein算子 k-泛函 强逆不等式 |
| 文章编号： | 0583-1431(2003)05-0891-06 |
| 修稿时间： | 2002-05-14 |
Strong Converse Inequality for Bernstein Operators |
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| Shun Sheng GUO Qiu Lan QI. Strong Converse Inequality for Bernstein Operators[J]. Acta Mathematica Sinica, 2003, 46(5): 891-896. DOI: cnki:ISSN:0583-1431.0.2003-05-007 |
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| Authors: | Shun Sheng GUO Qiu Lan QI |
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| Affiliation: | Shun Sheng GUO Qiu Lan QI(College of Mathematics and Information Science, Hebei Normal University, Shijiazhuang 050016, P. R. China) |
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| Abstract: | For Bernstein operators, we get the strong converse inequalities. Such inequalities have been proved by Ditzian Z., Ivanov K. G., Totik V. and Li Song with different methods. But these results are only normal estimates (with A = 1), the classical one (with A = 0) is not included. In this paper, we introduce the k-functional and extend the preuious results to a larger case 0< λ<1. |
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| Keywords: | Bernstein operator fc-functional Strong converse inequality |
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