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doi:10.1007/s11464-020-0819-z

Front. Math. China

2020, Vol. 15

Issue (1) : 127-140 https://doi.org/10.1007/s11464-020-0819-z

RESEARCH ARTICLE

Sharp distortion theorems for some subclasses of starlike mappings on

B P n

ℂ n

Xiaosong LIU¹(

), Taishun LIU²

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

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Abstract

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

Keywords Starlike mapping distortion theorem Jacobi determinant

Corresponding Author(s): Xiaosong LIU

Issue Date: 09 March 2020

Cite this article:

Xiaosong LIU,Taishun LIU. Sharp distortion theorems for some subclasses of starlike mappings on

B P n

ℂ n

[J]. Front. Math. China, 2020, 15(1): 127-140.

URL:

https://academic.hep.com.cn/fmc/EN/10.1007/s11464-020-0819-z
https://academic.hep.com.cn/fmc/EN/Y2020/V15/I1/127

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[1]	Qinghua XU, Taishun LIU, Xiaosong LIU. Sharp distortion theorems for a subclass of close-to-convex mappings[J]. Front Math Chin, 2013, 8(6): 1425-1436.
[2]	Jianfei WANG, Taishun LIU, Jin LU. Growth and distortion theorems on subclasses of quasi-convex mappings in several complex variables[J]. Front Math Chin, 2011, 6(5): 931-944.

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