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Vietnam Journal of Mathematics 40:1 (2012) 1-11

 

Uniqueness of Meromorphic Functions Sharing

Rational Functions with Their First Derivatives

Feng Lü1 and Jianming Qi2

1College of Science, China University of Petroleum, Qingdao,

Shandong, 266580, P. R. China

2Department of Mathematical and Physics, Shanghai Dianji University,

Shanghai, 201306, P. R. China

Received May 5, 2010

Revised December 26, 2011

Abstract. In this paper, by estimating the growth of ρn in a theorem of Pang and Zalcman, we obtain a uniqueness theorem of meromorphic functions which share two distinct rational functions with their first derivatives. It generalizes some previous related results of Rubel and Yang, Li and Yi, Qi, Lü and Chen, and so on.

2000 Mathematics Subject Classification. 30D35, 30D45.

Keywords.  Meromorphic functions, Nevanlinna theory, uniqueness, normal family, Marty’s criterion.

 

 

 

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