Ukrainian Mathematical Journal

, Volume 69, Issue 11, pp 1749–1761 | Cite as

On Rationally Loxodromic Holomorphic Functions

  • Dz. V. Lukivs’ka
  • A. Ya. Khrystiyanyn

We consider a functional equation of the form f(qz) = R(z)f(z), where R(z) is a rational function, z 𝜖 ℂ\{0}, q 𝜖 ℂ\{0}, |q| < 1. Holomorphic solutions of this equation are obtained. These solutions can be regarded as generalizations of p-loxodromic functions.


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© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • Dz. V. Lukivs’ka
    • 1
  • A. Ya. Khrystiyanyn
    • 1
  1. 1.Franko Lviv National UniversityLvivUkraine

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