MEROMORPHIC FUNCTIONS SHARING 1CM+1IM CONCERNING PERIODICITIES AND SHIFTS

Abstract

. The aim of this paper is to investigate the problems of meromorphic functions sharing values concerning periodicities and shifts. In this paper we prove the following result: Let f ( z ) and g ( z ) be two nonconstant entire functions, let c ∈ C \{ 0 } , and let a 1 , a 2 be two distinct finite complex numbers. Suppose that µ ( f ) (cid:54) = 1, ρ 2 ( f ) < 1, and f ( z ) = f ( z + c ) for all z ∈ C . If f ( z ) and g ( z ) share a 1 CM, a 2 IM, then f ( z ) ≡ g ( z ). Moreover, examples are given to show that all the conditions are neces-sary.