Abstract
In this article, we first establish the sharp distortion theorems of the Frechet derivative for a subclass of starlike mappings on the unit ball of complex Banach spaces and the bounded starlike circular domain in $\mathbb{C}^n$. Meanwhile, we also obtain the sharp distortion theorems of the Jacobi determinant for a subclass of starlike mappings on the bounded starlike circular domain in $\mathbb{C}^n$. Our derived conclusions are the generalizations of some known results in several complex variables and the classical results in one complex variable.
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