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Formal solutions of the generalized Dhombres functional equation with value one at zero

Abstract

We study formal solutions f of the generalized Dhombres functional equation \({f(zf(z)) = \varphi(f(z))}\). Unlike in the situation where f(0) = w 0 and \({w_0 \in \mathbb{C}{\setminus} \mathbb{E}}\) where \({\mathbb{E}}\) denotes the complex roots of 1, which were already discussed, we investigate solutions f where f(0) = 1. To obtain solutions in this case we use new methods which differ from the already existing ones.

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Correspondence to Jörg Tomaschek.

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Tomaschek, J., Reich, L. Formal solutions of the generalized Dhombres functional equation with value one at zero. Aequat. Math. 83, 117–126 (2012). https://doi.org/10.1007/s00010-011-0104-z

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Mathematics Subject Classification (2010)

  • Primary 30D05
  • 39B12
  • 39B32
  • Secondary 30B10

Keyword

  • Complex functional equations