Acta mathematica scientia,Series B ›› 2019, Vol. 39 ›› Issue (4): 1103-1120.doi: 10.1007/s10473-019-0414-0

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THE INVARIANCE OF SUBCLASSES OF BIHOLOMORPHIC MAPPINGS ON BERGMAN-HARTOGS DOMAINS

Yanyan CUI1, Hao LIU2   

  1. 1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou 466001, China;
    2. Institute of Contemporary Mathematics, Henan University, Kaifeng 475001, China
  • Received:2018-02-01 Revised:2018-08-06 Online:2019-08-25 Published:2019-09-12
  • Supported by:
    This work is supported by NSF of China (11271359, 11471098), Science and Technology Research Projects of Henan Provincial Education Department (17A110041), Scientific Research and Innovation Fund Projects of Zhoukou Normal University (ZKNUA201805).

Abstract: We mainly discuss the invariance of some subclasses of biholomorphic mappings under the generalized Roper-Suffridge operators on Bergman-Hartogs domains which are based on the unit ball Bn. Using the geometric properties and the distortion results of subclasses of biholomorphic mappings, we obtain the geometric characters of almost spirallike mappings of type β and order α, SΩ*(β, A, B), strong and almost spirallike mappings of type β and order α maintained under the generalized Roper-Suffridge operators on Bergman-Hartogs domains. Sequentially, we conclude that the generalized operators and the known operators preserve the same properties under some conditions. The conclusions generalize some known results.

Key words: Biholomorphic mappings, spirallike mappings, Bergman-Hartogs domain, Roper-Suffridge operator

CLC Number: 

  • 32A30
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