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On strongly starlikeness of order alpha in several complex variables. (English) Zbl 0926.32008
The authors introduce the concept of strong starlikeness of order $$\alpha > 0$$ for holomorphic mappings defined in the unit ball of $$\mathbb{C}^n$$. When $$\alpha \in (0,1]$$, strongly starlike mappings determine a subclass of starlike mappings, and the authors derive the sharp distortion and covering theorems. Finally, a connection is given between strong starlikeness and spirallikeness in $$\mathbb{C}^n$$.

##### MSC:
 32A30 Other generalizations of function theory of one complex variable 30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.) 32H99 Holomorphic mappings and correspondences