| $C^1$ Solutions of the Iterative Equation $G(x,f(x),\ldots,f^n(x))=F(x)$ |
| Received:January 31, 2010 Revised:May 28, 2010 |
| Key Words:
iterative equation Schr\"oder transformation contractive solution leading coefficient problem.
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| Fund Project:Supported by the Youth Foundation of Sichuan University (Grant No.2008123). |
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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. |
| Citation: |
| DOI:10.3770/j.issn:2095-2651.2012.01.013 |
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