A Note on Strongly Starlike Mappings in Several Complex Variables

Abstract

Let f be a normalized biholomorphic mapping on the Euclidean unit ball 𝔹n in ℂn 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.