On the Fekete and Szegö Problem for the Class of Starlike Mappings in Several Complex Variables

Abstract

Let $\mathcal{S}$ be the familiar class of normalized univalent functions in the unit disk. Fekete and Szegö proved the well-known result ${\max }_{f\in \mathcal{S}}\left|a_3-\lambda a_2^2\right|=1+2e^{-2\lambda /\mathrm{(1}-\mathrm{\lambda )}}$ for $\lambda \in \left[0, 1\right]$. We investigate the corresponding problem for the class of starlike mappings defined on the unit ball in a complex Banach space or on the unit polydisk in ${\mathbb{C}}^n$, which satisfies a certain condition.