Coefficients estimate for a subclass of holomorphic mappings on the unit polydisk in $\mathbb{C}^n$

Abstract

The aim of this paper is to obtain the sharp solutions of Fekete-Szeg\"{o} problems of high dimensional version for family of holomorphic mappings that are normalized on the unit polydisk $\mathbb{U}^n$ in $\mathbb{C}^n$. The main results unify some recent works, which are closely related to the starlike mappings. Moreover, some previous results are improved.