Volume 4,  Issue 1, 2003

Article 21

ON ENTIRE AND MEROMORPHIC FUNCTIONS THAT SHARE SMALL FUNCTIONS WITH THEIR DERIVATIVES

KIT-WING YU

RM 205, KWAI SHUN HSE., 
KWAI FONG EST., 
HONG KONG, CHINA.
E-Mail: maykw00@alumni.ust.hk

Received 28 February, 2002; Accepted 5 February, 2003.
Communicated by: H.M. Srivastava


ABSTRACT.    In this paper, it is shown that if $f$ is a non-constant entire function, $f$ and $f^{(k)}$ share the small function $a (\not \equiv 0, \infty)$ CM and $\delta(0, f)> \frac{3}{4}$, then $f \equiv f^{(k)}$. Furthermore, if $f$ is non-constant meromorphic, $f$ and $a$ do not have any common pole and $4\delta(0, f)+2(8+k)\Theta(\infty, f)>19+2k$, then the same conclusion can be obtained. Finally, some open questions are posed for the reader.
Key words:
Derivatives, Entire functions, Meromorphic functions, Nevanlinna theory, Sharing values, Small functions.

2000 Mathematics Subject Classification:
Primary 30D35.


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