On the Coefficient Inequality for A Subclass of Starlike Mappings in Several Complex Variables

摘要

Let S~* be the familiar class of normalized univalent functions in the unit disk.In [9], Keogh and Merkes proved that for a function f(z) = z +∑k=2∞ a_kz^k in the class S~*,then |a_3-λa_2~2| ≤ max{1, |3-4λ|}, λ∈ C. In this article, we investigate the corresponding problem for the subclass of starlike mappings defined on the unit ball in a complex Banach space, on the unit polydisk in Cnand the bounded starlike circular domain in C~■, respectively.