On rationally loxodromic holomorphic functions - Lukivska, Dz. V.; Khrystiyanyn, A. Ya. (Ukrains’kyi Matematychnyi Zhurnal, 2017)
We consider a functional equation of the form f(qz) = R(z)f(z), where R(z) is a rational function, z C{ 0}, q C{ 0}, | q| < 1. Holomorphic solutions of this equation are obtained. These solutions can be regarded as generalizations of p-loxodromic functions.