Normal Families of Zero-Free Meromorphic Functions - Yuntong Li (Abstract and Applied Analysis)
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 𝒟 such that for each 𝑓∈ℱ, 𝑓+𝑎(𝑓(𝑘))𝑛−𝑏 has at most 𝑛𝑘 zeros, ignoring multiplicity. Then ℱ is normal in 𝒟.