AbstractIn the paper there is considered a generalization of the well-known Fekete–Szegö type problem onto some Bavrin’s families of complex valued holomorphic functions of several variables. The definitions of Bavrin’s families correspond to geometric properties of univalent functions of a complex variable, like as starlikeness and convexity. First of all, there are investigated such Bavrin’s families which elements satisfy also a (j, k)-symmetry condition. As application of these results there is given the solution of a Fekete–Szegö type problem for a family of normalized biholomorphic starlike mappings in $${\mathbb {C}}^{n}.$$
C
n
.
The aim of this paper is to obtain the sharp solutions of Fekete-Szeg?
problems of high dimensional version for family of holomorphic mappings that
are normalized on the unit polydisk Un in Cn. The main results unify some
recent works, which are closely related to the starlike mappings. Moreover,
some previous results are improved.
Some results of Fekete–Szegö type for Bavrin’s families of holomorphic functions in $${\mathbb {C}}^{n}$$
