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- Title
The estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation in several complex variables.
- Authors
Liu, Xiao; Liu, Tai
- Abstract
In this paper, we obtain the estimates of all homogeneous expansions for a subclass of biholomorphic mappings which have parametric representation on the unit ball of complex Banach spaces. Meanwhile, we also establish the estimates of all homogeneous expansions for the above generalized mappings on the unit polydisk in C. Especially, the above estimates are only sharp for biholomorphic starlike mappings and starlike mappings of order α under restricted conditions. Our derived results generalize many known results.
- Subjects
BIHOLOMORPHIC mappings; COMPLEX variables; UNIT ball (Mathematics); BANACH spaces; STAR-like functions
- Publication
Acta Mathematica Sinica, 2017, Vol 33, Issue 2, p287
- ISSN
1439-8516
- Publication type
Article
- DOI
10.1007/s10114-016-5226-8