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Extremal Problems of Some Family of Holomorphic Functions of Several Complex Variables

College of Natural Sciences, Institute of Mathematics, University of Rzeszów, ul. Prof. Pigonia 1, 35-310 Rzeszów, Poland
Symmetry 2019, 11(10), 1304; https://doi.org/10.3390/sym11101304
Received: 25 September 2019 / Revised: 9 October 2019 / Accepted: 11 October 2019 / Published: 16 October 2019
Many authors, e.g., Bavrin, Jakubowski, Liczberski, Pfaltzgraff, Sitarski, Suffridge, and Stankiewicz, have discussed some families of holomorphic functions of several complex variables described by some geometrical or analytical conditions. We consider a family of holomorphic functions of several complex variables described in n-circular domain of the space C n . We investigate relations between this family and some of type of Bavrin’s families. We give estimates of G-balance of k-homogeneous polynomial, a distortion type theorem and a sufficient condition for functions belonging to this family. Furthermore, we present some examples of functions from the considered class. View Full-Text
Keywords: holomorphic functions; n-circular domains in Cn; Minkowski function; Bavrins families; growth and distortion theorems holomorphic functions; n-circular domains in Cn; Minkowski function; Bavrins families; growth and distortion theorems
MDPI and ACS Style

Trybucka, E. Extremal Problems of Some Family of Holomorphic Functions of Several Complex Variables. Symmetry 2019, 11, 1304.

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