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

Xiaosong LIU; Taishun LIU

doi:10.1007/s11464-020-0819-z

Front. Math. China ›› 2020, Vol. 15 ›› Issue (1) : 127 -140. DOI: 10.1007/s11464-020-0819-z

RESEARCH ARTICLE

Sharp distortion theorems for some subclasses of starlike mappings on $B P n$ in $ℂ n$

Xiaosong LIU ¹^,^†
, Taishun LIU ²

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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

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

B P n

ℂ n

. Front. Math. China, 2020, 15(1): 127-140 DOI:10.1007/s11464-020-0819-z

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