2018
Том 70
№ 8

All Issues

Lukivska Dz. V.

Articles: 2
Article (Ukrainian)

On rationally loxodromic holomorphic functions

Khrystiyanyn A. Ya., Lukivska Dz. V.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 11. - pp. 1505-1514

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 functions.

Brief Communications (Ukrainian)

Some holomorphic generalizations of loxodromic functions

Lukivska Dz. V.

↓ Abstract

Ukr. Mat. Zh. - 2017. - 69, № 9. - pp. 1284-1288

The functional equation of the form $f(qz) = p(z)f(z), z \in C\setminus \{ 0\} , q \in C\setminus \{ 0\} , | q| < 1$ is considered. For certain fixed elementary functions $p(z)$, holomorphic solutions of this equation are found. These solutions are some generalizations of loxodromic functions. Some of solutions are represented via the Schottky – Klein prime function.