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 \({\mathbb {C}}^{n}.\)

中文翻译：

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Fe $ {\ mathbb {C}} ^ {n} $$ C n中Bavrin的全纯函数族的Fekete–Szegö型的某些结果

在本文中，我们考虑了将众所周知的Fekete-Szegö型问题推广到几个变量的Bavrin的复值全纯函数的某些族。Bavrin族的定义对应于复杂变量的单价函数的几何特性，例如星形和凸性。首先，研究了这样的Bavrin族，这些族的元素也满足（j，  k）对称条件。作为这些结果的应用，给出了\（{\ mathbb {C}} ^ {n}。\}中一类归一化双全纯星形映射的Fekete–Szegö型问题的解决方案。