ABOUT BASILEVICH p -VALENTLY FUNCTIONS
The article deals with holomorphic functions in complete, bounded, multi-circular domains D ⊂ C n or in their subdomains D r =r D ( D is the closure of the domain D ) where r∈ 0,1 . The main idea of the study is to extend to the case of several complex variables p- valently Basilevich functions of type μ and order α of one complex variable B D (p) μ ,α . Examples of new subclasses B D (p ) μ ,α are considered and the conditions of belonging of functions to these subclasses are determined. Some relations between the Basilevich classes B D (p) μ ,α (μ,α) and M D p λ,μ,A,B are given, as well as various useful properties and characteristics of the class M D p λ,μ,A,B for the multidimensional case, using the Briot-Bouquet differential subordination method.