Some Results on Unicity of Entire Functions Related to Normal Families

IntroductionLet D be a domain in C.Define for f mero-morphic on D and a,b∈C,we putE(a,f)={z∶f(z)-a=0}where a zero of multiplicity m is counted m times inthe set.And put-E(a,f)=f-1({a})∩D={z∈D∶f(z)=a}Then f and g share a IM(ignoring multiplicities),i.e.-E(a,f)=-E(a,g)If f-a and g-a have the same zeros with thesame multiplicities,then f and g share the value aCM(counting multiplicities),i.e.E(a,f)=E(a,g)A meromorphic function f on C is called anormal function if there exists a posit…

Some Results on Unicity of Entire Functions Related to Normal Families

This paper studied the connection between normal family and unicity, and proved some results on unicity of entire functions. Mostly, it was proved: Let f be a nonconstant entire function, and let a, c be two nonzero complex numbers. If E(a,f)=E(a,f), and f"(z)=c whenever f' (z)=a, then f(z)=Aecz/a+ac-a2/c. The proof uses the theory of normal families in an essential way.