On the Fekete and Szegö problem for the class of starlike mappings in several complex variables (Q1725028)

Summary: Let \(\mathcal{S}\) be the familiar class of normalized univalent functions in the unit disk. Fekete and Szegö proved the well-known result \(\max_{f \in \mathcal{S}} \left|a_3 - \lambda a_2^2\right| = 1 + 2 e^{- 2 \lambda /(1 - \lambda}\) 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.