| LIMIT OF ITERATES FOR BERNSTEIN POLYNOMIALS DEFINED ON A TRIANGLE |
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| 引用本文： | 陈发来 冯玉瑜. LIMIT OF ITERATES FOR BERNSTEIN POLYNOMIALS DEFINED ON A TRIANGLE[J]. 高校应用数学学报(英文版), 1993, 8(1): 45-53. DOI: 10.1007/BF02661990 |
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| 作者姓名： | 陈发来 冯玉瑜 |
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| 作者单位： | DepartmentofMathematics,UnversityofScienceandTechnologyofChina,Hefei230026 |
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| 摘 要： | Let f∈C[0,1],and Bn(f,x) be the a-th Bernstein polynomial associated with function f.ln 1967,the limit of iterates for B.(f,x) was given by Kelisky and Rivlin.After this,Many mathematicians studied and generalized this result.But anyway,all these discussions are only for univariate case ,In this paper,the main contrlbution is that the limit of lterates for Bernstein polynomial defined on a triangle is given completely.
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| 关 键 词： | 伯恩斯坦多项式 渐进公式 有限迭代 线性算子 |
| 收稿时间： | 1991-12-03 |
Limit of iterates for bernstein polynomials defined on a triangle |
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| Chen Falai,Feng Yuyu. Limit of iterates for bernstein polynomials defined on a triangle[J]. Applied Mathematics A Journal of Chinese Universities, 1993, 8(1): 45-53. DOI: 10.1007/BF02661990 |
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| Authors: | Chen Falai Feng Yuyu |
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| Affiliation: | (1) Department of Mathematics, University of Science and Technology of China, 230026 Hefei |
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| Abstract: | Letf∈C[0,1], andB n(f,x) be then-th Bernstein polynomial associated with functionf. In 1967, the limit of iterates forB n(f,x) was given by Kelisky and Rivlin. After this, Many mathematicians studied and generalized this result. But anyway, all these discussions are only for univariate case. In this paper, the main contribution is that the limit of iterates for Bernstein polynomial defined on a triangle is given completely. Supported by National Education Committee Foundation and NSF. |
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| Keywords: | Bernstein Polynomial Asymptotical Formula Limit of Iterates. |
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