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

Read more about this topic:  Schwarzian Derivative

Famous quotes containing the word conditions:

    People nowadays have such high hopes of America and the political conditions obtaining there that one might say the desires, at least the secret desires, of all enlightened Europeans are deflected to the west, like our magnetic needles.
    —G.C. (Georg Christoph)