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Growth and covering theorems for a class of strongly and almost starlike mappings of order \(\alpha\). (Chinese. English summary) Zbl 1313.32010

Summary: In this paper, the authors study a class of special strongly and almost starlike mappings of order \(\alpha\). They give the definition of strongly and almost spirallike mapping of type \(\beta\) and order \(\alpha\) by combining the geometrical characteristic of strongly and almost starlike mappings of order \(\alpha\) and spirallike mappings of type \(\beta\). And from the geometrical characteristic of mappings, they obtain the growth and covering theorems for strongly and almost spirallike mappings of type \(\beta\) and order \(\alpha\) on the unit ball in complex Banach spaces.

MSC:

32A30 Other generalizations of function theory of one complex variable
32H02 Holomorphic mappings, (holomorphic) embeddings and related questions in several complex variables
30C45 Special classes of univalent and multivalent functions of one complex variable (starlike, convex, bounded rotation, etc.)
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