| 迭代函数方程$G(x,f(x),\ldots,f^n(x))=F(x)$的$C^1$解 |
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| 引用本文： | 陈敬敏,陈丽.迭代函数方程$G(x,f(x),\ldots,f^n(x))=F(x)$的$C^1$解[J].数学研究及应用,2012,32(1):119-126. |
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| 作者姓名： | 陈敬敏 陈丽 |
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| 作者单位： | 四川大学数学学院, 四川 成都 610064;四川大学数学学院, 四川 成都 610064 |
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| 基金项目： | 四川大学青年基金 (Grant No.2008123). |
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| 摘 要： | In this paper we consider the iterative equation G(x,f(x),...,f n(x)) = F(x) on R,and give the existence of C 1 solutions near the fixed point of F,which generalize some results on the leading coefficient problem from the form of the polynomial-like iterative equations to the general form.
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| 关 键 词： | iterative equation Schro¨der transformation contractive solution leading coefficient problem. |
| 收稿时间： | 2010/1/31 0:00:00 |
| 修稿时间： | 2010/5/28 0:00:00 |
$C^1$ Solutions of the Iterative Equation $G(x,f(x),\ldots,f^n(x))=F(x)$ |
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| Jing Min CHEN and Li CHEN.$C^1$ Solutions of the Iterative Equation $G(x,f(x),\ldots,f^n(x))=F(x)$[J].Journal of Mathematical Research with Applications,2012,32(1):119-126. |
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| Authors: | Jing Min CHEN and Li CHEN |
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| Institution: | Department of Mathematics, Sichuan University, Sichuan 610064, P. R. China |
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| Abstract: | In this paper we consider the iterative equation $G(x,f(x),\ldots,f^n(x))=F(x)$ on ${\mathbb{R}}$, and give the existence of $C^1$ solutions near the fixed point of $F$, which generalize some results on the leading coefficient problem from the form of the polynomial-like iterative equations to the general form. |
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| Keywords: | iterative equation Schr\"oder transformation contractive solution leading coefficient problem |
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