On the value distribution of $\varphi(z) f^{n-1}(z)f^{(k)}(z)$

Volume 3, Issue 1, 2002

Article 8

ON THE VALUE DISTRIBUTION OF

UNITED CHRISTIAN COLLEGE
11 TONG YAM STREET, TAI HANG TUNG,
SHAMSHUIPO, KOWLOON,
HONG KONG, CHINA
E-Mail: maykw00@alumni.ust.hk

Received 01 May, 2001; 04 October, 2001.
Communicated by: H. M. Srivastava

ABSTRACT. In this paper, the value distribution of $\varphi(z) [f(z)]^{n-1}f^{(k)}(z)$ is studied, where

is a transcendental meromorphic function, $\varphi(z) (\not \equiv 0)$ is a function such that $T(r, \varphi)=o(T(r, f))$ as $r \to +\infty$ ,

and

are positive integers such that

or $n \ge k+3$ . This generalizes a result of Hiong.

Key words:
Derivatives, Inequality, Meromorphic Functions, Small Functions, Value Distribution

2000 Mathematics Subject Classification:
30D35, 30A10.

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