| 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 |
| 迭代函数方程$G(x,f(x),\ldots,f^n(x))=F(x)$的$C^1$解 |
| $C^1$ Solutions of the Iterative Equation $G(x,f(x),\ldots,f^n(x))=F(x)$ |
| 投稿时间：2010-01-31 修订日期：2010-05-28 |
| DOI：10.3770/j.issn:2095-2651.2012.01.013 |
| 中文关键词: 迭代方程 Schr\"oder 变换 压缩解 首项系数问题. |
| 英文关键词:iterative equation Schr\"oder transformation contractive solution leading coefficient problem. |
| 基金项目:四川大学青年基金 (Grant No.2008123). |
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| 中文摘要: |
| 本文在实数范围内研究了迭代函数方程$G(x,f(x),\ldots,f^n(x))=F(x)$, 给出了在$F$的不动点附近的$C^1$解, 将多项式型迭代函数方程中首项系数问题的相关结论推广到更一般的形式. |
| 英文摘要: |
| 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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