A Function-Sharing Criterion for Normal Functions

2025/09/20 by Gopal Datt, Datt, Gopal, Pal, Ritesh +1
Computer Science · #30D45 #Complex Variables (math.CV) #FOS: Mathematics #Numerical Methods and Algorithms #Parallel Computing and Optimization Techniques

paper · pdf · doi:10.48550/arxiv.2509.16740

openalex publication_date 2025/09/20 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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 \mathbbD⊂ ℂ, ψ₁, ψ₂, and ψ₃ be three meromorphic functions in the unit disc \mathbbD, continuous on ∂\mathbbD:=\z∈ℂ : |z|=1\, such that ψ_i(z)≠ψ_j(z) (1≤ i

Citations

• Normal families and quasiregular mappings
• Sharing of a set of meromorphic functions and Montel's theorem

Related

• Normality Criteria for Families of Meromorphic Functions about Shared Functions
• Normality through partial sharing of sets with differential polynomials
• A normality criterion generalizing Gu's result
• Normality from one family of meromorphic functions to another through sharing of values
• Further results on normal families of meromorphic functions concerning shared values