On rationally loxodromic holomorphic functions

• Date: 2017
• Main Authors: Lukivska, Dz. V., Khrystiyanyn, A. Ya., Луківська, Дз. В., Христіянин, А. Я.
• Format: Article
• Language: Ukrainian
• Published: Institute of Mathematics, NAS of Ukraine 2017
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1798
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

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