Normal Families of Zero-Free Meromorphic Functions

Abstract EN

Let a(≠0), b∈ℂ, and n and k be two positive integers such that n≥2.

Let ℱ be a family of zero-free meromorphic functions defined in a domain ? such that for each f∈ℱ, f+a(f(k))n−b has at most nk zeros, ignoring multiplicity.

Then ℱ is normal in ?.