A Function-Sharing Criterion for Normal Functions

In this paper, we present a function-sharing criterion for the normality of meromorphic functions. Let f be a meromorphic function in the unit disc D⊂ C, ψ₁, ψ₂, and ψ₃ be three meromorphic functions in the unit disc D, continuous on ∂D:=\,:\,|z|=1\, such that ψᵢ(z)≠ψⱼ(z) (1≤ i<j≤ 3) . We prove that, if ψ₁, ψ₂, and ψ₃ share the function f on D, then f is normal. Building upon this, we further establish an additional criterion for normal functions.