Normality Criteria of Meromorphic Functions That Share a Holomorphic Function

Abstract EN

Let F be a family of meromorphic functions defined in D, let ψ(≢0), a0,a1,...,ak-1 be holomorphic functions in D, and let k be a positive integer.

Suppose that, for every function f∈F, f≠0, P(f)=f(k)+ak-1f(k-1)+⋯+a1f'+a0f≠0 and, for every pair functions (f,g)∈F, P(f), P(g) share ψ, then F is normal in D.