### A criterion of univalence in $C^n$ in terms of the Schwarzian derivative

#### Abstract

By using the using the Loewner Chain Theory, we obtain a new criterion of univalence in $C^n$ in terms of the Schwarzian derivative introduced in [3] by using the arguments in [8]. We as well derive explicitly the formula given in [3] by relating the Schwarzian derivative with the numerical method of approximation of zeros due to Halley.

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DOI: http://dx.doi.org/10.24193/subbmath.2022.2.16

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