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New subclasses of biholomorphic mappings and the modified Roper-Suffridge operator

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Abstract

The authors propose a new approach to construct subclasses of biholomorphic mappings with special geometric properties in several complex variables. The Roper-Suffridge operator on the unit ball B n in Cn is modified. By the analytical characteristics and the growth theorems of subclasses of spirallike mappings, it is proved that the modified Roper-Suffridge operator [Φ G,γ (f)](z) preserves the properties of S *Ω (A,B), as well as strong and almost spirallikeness of type β and order α on B n. Thus, the mappings in S *Ω (A,B), as well as strong and almost spirallike mappings, can be constructed through the corresponding functions in one complex variable. The conclusions follow some special cases and contain the elementary results.

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Authors and Affiliations

  1. College of Mathematics and Statistics, Zhoukou Normal University, Zhoukou, Henan, 466001, China

    Chaojun Wang & Yanyan Cui

  2. Institute of Contemporary Mathematics, Henan University, Kaifeng, Henan, 475001, China

    Hao Liu

Authors
  1. Chaojun Wang
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  2. Yanyan Cui
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  3. Hao Liu
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Corresponding author

Correspondence to Chaojun Wang.

Additional information

This work was supported by the National Natural Science Foundation of China (Nos. 11271359, 11471098), the Joint Funds of the National Natural Science Foundation of China (No.U1204618) and the Science and Technology Research Projects of Henan Provincial Education Department (Nos. 14B110015, 14B110016).

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Wang, C., Cui, Y. & Liu, H. New subclasses of biholomorphic mappings and the modified Roper-Suffridge operator. Chin. Ann. Math. Ser. B 37, 691–704 (2016). https://doi.org/10.1007/s11401-016-1005-1

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  • DOI: https://doi.org/10.1007/s11401-016-1005-1

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