A Note on Strongly Starlike Mappings in Several Complex Variables

Abstract

Let $f$ be a normalized biholomorphic mapping on the Euclidean unit ball ${𝔹}^n$ in ${ℂ}^n$ and let $\alpha \in \left(\mathrm{0,1}\right)$. In this paper, we will show that if $f$ is strongly starlike of order $\alpha$ in the sense of Liczberski and Starkov, then it is also strongly starlike of order $\alpha$ 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 $n\ge 2$.