| 一般隐函数组定理的证明 |
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| 引用本文： | 刘小妹,于俊杰.一般隐函数组定理的证明[J].江西科学,2012,30(4):427-428,437. |
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| 作者姓名： | 刘小妹 于俊杰 |
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| 作者单位： | 1. 九江学院理学院数学系,江西九江,332005
2. 九江学院图书馆,江西九江,332005 |
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| 摘 要： | 在数学分析教材中已有隐函数定理及一般隐函数组定理的证明,文1]通过压缩映射证明了隐函数定理。借助矩阵范数与向量范数的表示形式,应用Banach不动点定理证明一般隐函数组定理,其证明过程比数学分析教材中原有的证明过程更为清晰、易懂。
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| 关 键 词： | 压缩映射 不动点定理 一般隐函数组定理 |
Proof on the Theorem of System of General Implicit Function |
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| LIU Xiao-mei,YU Jun-jie.Proof on the Theorem of System of General Implicit Function[J].Jiangxi Science,2012,30(4):427-428,437. |
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| Authors: | LIU Xiao-mei YU Jun-jie |
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| Institution: | 1.College of Science,Jiujiang University,Jiangxi Jiujiang 332005 PRC; 2.Library of Jiujiang University,Jiangxi Jiujiang 332005 PRC) |
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| Abstract: | There were the proof about the Theorem of System of Implicit Function and General Implicit Function in the mathematical analysis teaching materies,The paper1] proved the Implicit Function Theorem by the Compression Mapping.This paper will prove the Theorem of System of General Implicit Function by Banach Fixed Point Theorem,with the help of the representation of Matrix Norm and Vector Norm.The proof is clearer and more easy to understand than the original proof of the mathematical analysis. |
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| Keywords: | Compression mapping Fixed point theorem The theorem of system of general implicit function |
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