A Normality Criterion of Meromorphic Functions Related to Sharing a Value

This paper mainly obtains the following result:let F be a family of meromorphic functions on a domain D in the complex plane,a,b be finite non-zero complex numbers such that f-a has only zeros multiplicity at least k for each f in F.If for each f in F,f(z)=a■f(k)(z)=a,f(k)(z)=b■f(k+1)(z)=b,then for k≥3,F is normal in D and for k=2 and a/b≠4,F is normal in D.An example is given to illustrate the condition of a/b≠4 is necessary.