Research Article
Normality of Composite Analytic Functions and Sharing an Analytic Function
1 Shaozhou Normal College, Shaoguan University, Shaoguan 512009, China
2 Department of Mathematics, Xinjiang Normal University, Urumqi 830054, China
3 School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, China
Fixed Point Theory and Applications 2010, 2010:417480 doi:10.1155/2010/417480
Published: 18 October 2010Abstract
A result of Hinchliffe (2003) is extended to transcendental entire function, and an
alternative proof is given in this paper. Our main result is as follows: let 
be an analytic function, 
a family of analytic functions in a domain 
, and 
a transcendental entire function. If 
and 
share 
IM for each pair 
, and one of the following conditions holds: (1) 
has at least two distinct zeros for any 
; (2) 
is nonconstant, and there exists 
such that 
has only one distinct zero 
, and suppose that the multiplicities 
and 
of zeros of 
and 
at 
, respectively, satisfy 
, for each 
, where 
; (3) there exists a 
such that 
has no zero, and 
is nonconstant, then 
is normal in 
.
