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In 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 .

Some results of Fekete–Szegö type for Bavrin’s families of holomorphic functions in $${\mathbb {C}}^{n}$$