Chinese Quarterly Journal of Mathematics ›› 2016, Vol. 31 ›› Issue (2): 211-220.doi: 10.13371/j.cnki.chin.q.j.m.2016.02.012

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Growth Theorem and Distortion Theorem for a Subclass of Parabolic Starlike Mappings

  

  1. College of Mathematics and Information Science, Pingdingshan University.  Department of Information Engineering, Xuchang Vocational Technical College
  • Received:2015-09-03 Online:2016-06-30 Published:2020-11-09
  • About author:ZHANG Xiao-fei(1982-), male, native of Xuchang, Henan, a lecturer of Pingdingshan University, Ph.D., engages in function theory of several complex variables.
  • Supported by:
    Supported by the Doctoral Foundation of Pingdingshan University(PXY-BSQD-2015005); Supported by the Natural Science Foundation of Zhejiang Province(Y14A010047); Supported by the the Key Scientific Research Projects in Universities of Henan Province(16B110010); Supported by the Foster Foundation of Pingdingshan University(PXY-PYJJ2016007);

Abstract: In this article, we firstly introduce a subclass of parabolic starlike mappings writen as PS(β; ρ).Secondly,the growth theorem for PS(β; ρ) on the unit ball in complex Banach space is obtained. Finaly, as the application of the growth theorem of PS(β; ρ), the distortion theorem along a unit direction is also established. 

Key words: parabolic starlike mappings, growth theorem, distortion theorem

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