THE INVARIANCE OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE β AND ORDER α

doi:10.1016/S0252-9602(15)30066-7

Abstract

Abstract:

The invariance of strong and almost spirallike mappings of type β and order α is discussed in this paper. From the maximum modulus principle of holomorphic functions, we obtain that the generalized Roper-Suffridge operators preserve strong and almost spirallikeness of type β and order α on the unit ball Bⁿ in Cⁿ and on bounded and complete Reinhardt domains. Therefore we obtain that the generalized Roper-Suffridge operators preserve strong spirallikeness of type β, strong and almost starlikeness of order α, strong starlikeness on the corresponding domains.Thus we can construct more subclasses of spirallike mappings in several complex variables.

Key words: strong and almost spirallike mappings of type β and order α, Roper-Suffridge operators, homogeneous expansion

CLC Number:

32A30

Yanyan CUI, Chaojun WANG, Hao LIU. THE INVARIANCE OF STRONG AND ALMOST SPIRALLIKE MAPPINGS OF TYPE β AND ORDER α[J].Acta mathematica scientia,Series B, 2015, 35(6): 1454-1466.

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