98-28   Berichtsreihe des Mathematischen Seminars der Universität Kiel

Walter Bergweiler:

Normality and exceptional values of derivatives

We show that a family $\FF$ of functions meromorphic in some domain is normal, if for all $f\in\FF$ the derivative $f'$ omits the value $1$ and if the values that $f'$ can take at the zeros of $f$ satisfy certain restrictions. As an application we obtain a new proof of a theorem of Langley which classifies the functions $f$ meromorphic in the plane such that $f$ and $f''$ have no zeros.

Mathematics Subject Classification (1991): 30D45, 30D30

Bibliographical note: Proc. Amer. Math. Soc. 129, 121-129 (2001)

Mail an Jens Burmeister
[Thu Feb 19 18:56:34 2009]