On Entire and Meromorphic Functions that Share Small Functions with their Derivatives

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

is a non-constant entire function,

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

is non-constant meromorphic,

and

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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