| 关于Weierstrass一致逼近定理的证明 |
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| 引用本文： | 谷峰,张维珊,谷敏芳.关于Weierstrass一致逼近定理的证明[J].齐齐哈尔大学学报(自然科学版),1991(1). |
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| 作者姓名： | 谷峰 张维珊 谷敏芳 |
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| 作者单位： | 黑龙江省林业管理干部学院
(谷峰)，黑龙江省农行齐齐哈尔干校
(张维珊)，绥化地区安达技校(谷敏芳) |
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| 摘 要： | 本文将Bernstein定理进行了推广,并用其证明了Weierstrass一致逼近定理,从而很直观地说明了Ca,b]中的函f(x)不仅可被代数多项式一致逼近,而且也可被函数多项式一致逼近。此外,我们还给出了Weierstrass一致逼近定理的另外一种证明。
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| 关 键 词： | 连续函数 一致逼近 |
On Proof of Weierstrass'Uniform Approximation Theorem |
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| Gu Feng.On Proof of Weierstrass'Uniform Approximation Theorem[J].Journal of Qiqihar University(Natural Science Edition),1991(1). |
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| Authors: | Gu Feng |
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| Institution: | Gu Feng (Forestry Management College of Heilongjiang)
Zhang Weishan (Agriculture Bank College of Qiqihar Heilongjiang)
Gu Minfang (Suihua Technological School at Anda) |
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| Abstract: | The article continues to spread the theorem of Bernstein,and uses it to prove the uniform approximation theorem of Weierstrass. Thus it directly expresses the fanction f ( x ) in C a, b] not only to be approximated uniformly by algebraic polynomials but also by functional polynomials. Jn addition, the spread of Bernstein's theorem can be proved easily by Bernstein's theorem. The article can offer another proof. |
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| Keywords: | Continuous function Uniform approximation |
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