Analytic solutions of a functional equation for invariant curves (Q5945751)
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scientific article; zbMATH DE number 1657541
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Analytic solutions of a functional equation for invariant curves |
scientific article; zbMATH DE number 1657541 |
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Analytic solutions of a functional equation for invariant curves (English)
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11 September 2002
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invariant curves
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power series solutions
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analytic solutions
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iterative functional equation
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0.94610894
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0.9288522
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0.92706895
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0.9231695
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The authors prove the existence of analytic solutions for the iterative functional equation NEWLINE\[NEWLINEf\bigl(f(x) \bigr)=2f(x)-x-\frac 12 \biggl(g\bigl( f(x)\bigr)+g(x) \biggr),\;x\in\mathbb{R}, \tag{1}NEWLINE\]NEWLINE [cf. \textit{C. T. Ng} and \textit{W. Zhang}, J. Difference Equ. Appl. 3, No. 2, 147-168 (1997; Zbl 0891.34070)], by locally reducing the equation to another functional equation without iteration, called the auxiliary equation of (1), and by constructing solutions in uniformly convergent power series for this auxiliary equation.
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