Computational Methods and Function Theory 1 (2001), No. 2, 301--310
Copyright Heldermann Verlag 2001
Djamel Benbourenane
dbenbour@iusb.edu, Mathematical Sciences Indiana University South Bend, 1700 Mishawaka Ave., P. O. Box 7111 South Bend, IN 46634, U.S.A.
Risto Korhonen
rkorhone@cc.joensuu.fi, University of Joensuu, Department of Mathematics, P. O. Box 111, FIN-80101 Joensuu, Finland.
We will prove that the inequality \begin{equation*} m\!\brac{r,\frac{f'}{f}} \leq \log^{+}\! \brac{\frac{T(\rho,f)}{r} \frac{\rho}{\rho-r}} + 5.3078, \end{equation*} where $\rho > r$, holds for all meromorphic functions such that $f(0)=1$. This is an improvement of an earlier result by Gol'dberg and Grinshtein \cite{gogr}.
Keywords: Logarithmic derivative, error term, growth, meromorphic function.
MSC 2000: Primary 30D35.
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