ON SOME GENERALIZATIONS OF P-LOXODROMIC FUNCTIONS

A. Ya. Khrystiyanyn, Dz. V. Lukivska

Анотація


Розглянуто функцiональне рiвняння f(qz) - p(z)f(z), z   \ {0} ,q   \ {0}, q<1. При певних фiксованих елементарних функцiях p(z) знайдено його мероморфнi та голоморфнi розв’язки. Цi розв’язки є деякими узагальненнями p-локсодромних функцiй.

The functional equation of the form f(qz) - p(z)f(z), z   \ {0} ,q   \ {0}, q<1 is considered. For certain fixed elementary functions p(z), meromorphic as well as holomorphic solutions of this equation are found. These solutions are some generalizations of p-loxodromic functions.


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