A Note on Strongly Starlike Mappings in Several Complex Variables

Abstract EN

Let f be a normalized biholomorphic mapping on the Euclidean unit ball ? n in ℂ n and let α ∈ 0,1 .

In this paper, we will show that if f is strongly starlike of order α in the sense of Liczberski and Starkov, then it is also strongly starlike of order α in the sense of Kohr and Liczberski.

We also give an example which shows that the converse of the above result does not hold in dimension n ≥ 2 .