Schwarzian Derivative - Conditions For Univalence

Conditions For Univalence

If f(z) is a holomorphic function on the unit disc |z| < 1, then W. Kraus (1932) and Nehari (1949) proved that a necessary condition for f to be univalent is

Conversely if f(z) is a holomorphic function on the unit disc satisfying

then Nehari proved that f is univalent.

In particular a sufficient condition for univalence is

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