A Normality Criterion for Meromorphic Functions with One of Its Differential Polynomials

In this paper we obtain the following results: 1.Take positive integers n,k≥2.Let F be a family of meromorphic functions defined on a domain D in the complex plane,such that each f∈F has only zeros of multiplicity at least k.For each pair f,g in F,fLn(f) and gLn(g) share a non-zero complex value a ignoring multiplicity.Then F is normal on D,where L(f) is defined f(k)+a1f(k-1)+…+akf,in which a1,…,ak are constants.2.Take positive integers n and k with n≥2 and take a non-zero complex number a.Let F be a family of meromorphic functions in the plane domain D such that each f∈F has only zeros of multiplicity at least k.For each element f of F,if fLn(f(z))=a implies |f(k)(z)|≤A for a positive number A,then F is normal in D.