PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS

doi:10.1016/S0252-9602(16)30104-7

Acta mathematica scientia,Series B ›› 2016, Vol. 36 ›› Issue (6): 1767-1779.doi: 10.1016/S0252-9602(16)30104-7

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PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS

Chaojun WANG¹, Yanyan CUI¹, Hao LIU²

1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
2. College of Mathematics and Statistics, Henan University, Kaifeng 475001, China

Received:2015-05-08 Revised:2016-04-06 Online:2016-12-25 Published:2016-12-25
Contact: Hao LIU,E-mail:haoliu@henu.edu.cn E-mail:haoliu@henu.edu.cn
Supported by:
This work was supported by NSFC (11271359, U1204618), Science and Technology Research Projects of Henan Provincial Education Department (14B110015, 14B110016), Youth Fund Projects of Zhoukou Normal University (zknuB3201608).

Abstract

Abstract:

In this paper, we mainly discuss the properties of the modified Roper-Suffridge operators on Reinhardt domains. By the analytical characteristics and distortion results of subclasses of biholomorphic mappings, we conclude that the modified Roper-Suffridge operators preserve the properties of S_Ω^*(β, A, B), almost starlike mapping of complex order λ on Ω_{n,p₂,…,p_n}. Sequentially, we get that the modified Roper-Suffridge operators preserve spirallikeness of type β and order α, strongly pirallikeness of type β and order α, almost starlikeness of order α on Ω_{n,p₂,…,p_n}. The conclusions provide a new approach to construct these biholomorphic mappings which have special geometric properties in several complex variables.

Key words: Roper-Suffridge operator, spirallike mappings, starlike mappings

CLC Number:

32A30

Chaojun WANG, Yanyan CUI, Hao LIU. PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS[J].Acta mathematica scientia,Series B, 2016, 36(6): 1767-1779.

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References

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PROPERTIES OF THE MODIFIED ROPER-SUFFRIDGE EXTENSION OPERATORS ON REINHARDT DOMAINS

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