We consider a functional equation of the form f(qz) = R(z)f(z), where R(z) is a rational function, z đťś– â„‚\{0}, q đťś– â„‚\{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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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, No. 11, pp. 1505–1514, November, 2017.
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Lukivs’ka, D.V., Khrystiyanyn, A.Y. On Rationally Loxodromic Holomorphic Functions. Ukr Math J 69, 1749–1761 (2018). https://doi.org/10.1007/s11253-018-1467-2
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DOI: https://doi.org/10.1007/s11253-018-1467-2