Frontiers of Mathematics in China >

2020 , Vol. 15 >Issue 1: 127 - 140

DOI: https://doi.org/10.1007/s11464-020-0819-z

RESEARCH ARTICLE

Sharp distortion theorems for some subclasses of starlike mappings on BPn in ℂn

  • Xiaosong LIU , 1 ,
  • Taishun LIU 2
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  • 1. School of Mathematics and Statistics, Lingnan Normal University, Zhanjiang 524048, China
  • 2. Department of Mathematics, Huzhou University, Huzhou 313000, China

Received date: 28 Aug 2019

Accepted date: 30 Jan 2020

Published date: 15 Feb 2020

Copyright

2020 Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature
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Abstract

We mainly establish the distortion theorems of Jacobi determinant for three subclasses of starlike mappings on BPn; where BPn={z=(z1,...,zn)T∈ℂn:∑l=1n|zl|p<1},p>1: In particular, the above distortion theorems are sharp if BPn is the unit polydisk in ℂn: Our results reduce to the corresponding classical results in one dimension of complex function theory.

Key words： Starlike mapping; distortion theorem; Jacobi determinant

Cite this article

Xiaosong LIU , Taishun LIU . Sharp distortion theorems for some subclasses of starlike mappings on BPn in ℂn[J]. Frontiers of Mathematics in China, 2020 , 15(1) : 127 -140 . DOI: 10.1007/s11464-020-0819-z

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