Normal families of meromorphic functions sharing one function

摘要

Suppose p ( z ) is a holomorphic function, the multiplicity of its zeros is at most d, P ( z ) is a nonconstant polynomial. Let ? be a family of meromorphic functions in a domain D, all of whose zeros and poles have multiplicity at least max { k 2 + d + 1 , k + d } . If for each pair of functions f and g in ?, P ( f ) f ( k ) and P ( g ) g ( k ) share a holomorphic function p ( z ) , then ? is normal in D. It generalizes and extends the results of Jiang, Gao and Wu, Xu. MSC:30D35, 30D45.