ON THE SHARP GROWTH, COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN Cn

doi:10.1016/S0252-9602(07)60077-0

Acta mathematica scientia,Series B

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ON THE SHARP GROWTH, COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN Cⁿ

Liu Xiaosong; Liu Taishun

School of Mathematics and Computation Science, Zhanjiang Normal University, Zhanjiang 524048, China

Received:2005-10-08 Revised:2006-03-23 Online:2007-10-20 Published:2007-10-20
Contact: Liu Xiaosong

Abstract

Abstract:

In this article, a normalized biholomorphic mapping f defined on bounded starlike circular domain in Cⁿ is considered, where z=0 is a zero of order k+1 of f(z)-z. The sharp growth, covering theorems for almost starlike mappings of order α and starlike mappings of order α are established. Meanwhile, the
construction of the above mappings on bounded starlike circular domain in Cⁿ is also discussed, it provides the extremal mappings for the growth, covering theorems of the above mappings.

Key words: Zero of order k+1, normalized biholomorphic mappings, almost starlike mappings of order α, starlike mappings of order α, growth, covering theorems

CLC Number:

30C25

Liu Xiaosong; Liu Taishun. ON THE SHARP GROWTH, COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN Cⁿ[J].Acta mathematica scientia,Series B, 2007, 27(4): 803-812.

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ON THE SHARP GROWTH, COVERING THEOREMS FOR NORMALIZED BIHOLOMORPHIC MAPPINGS IN Cⁿ

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