摘要:We study the normality of families of meromorphic functions related to a Hayman conjecture. We consider whether a family of meromorphic functions ℱ is normal in 𝐷 if, for every pair of functions 𝑓 and 𝑔 in ℱ, 𝑓−𝑎𝑓𝑛 and 𝑔−𝑎𝑔𝑛 share the value 𝑏 for 𝑛=1,2, and 3, where 𝑎 and 𝑏≠0 are two finite complex numbers. Some examples show that the conditions in our results are the best possible.