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

Abstract EN

Let S be the familiar class of normalized univalent functions in the unit disk.

Fekete and Szegö proved the well-known result max f ∈ S a 3 - λ a 2 2 = 1 + 2 e - 2 λ / (1 - λ) for λ ∈ 0 ,   1 .

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 C n , which satisfies a certain condition.