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An estimate for the iterates of \(C^ m\)-functions with fixed point \(0\). (English) Zbl 1063.39017

Summary: We provide an estimate for the iterates of analytic functions and of \(C^m\) functions with fixed point 0. We use a method of E. Jabotinsky [Trans. Am. Math. Soc. 108, 457–477 (1963; Zbl 0113.28303)] which yields the explicit representation of the coefficients of the iterates of analytic functions.

MSC:

39B12 Iteration theory, iterative and composite equations
30D05 Functional equations in the complex plane, iteration and composition of analytic functions of one complex variable

Citations:

Zbl 0113.28303
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References:

[1] DOI: 10.1090/S0002-9947-1963-0155971-X
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