A Function-Sharing Criterion for Normal Functions
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866915504704192512 |
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| author | Datt, Gopal Pal, Ritesh Trivedi, Ashish Kumar |
| author_facet | Datt, Gopal Pal, Ritesh Trivedi, Ashish Kumar |
| contents | 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 $\mathbb{D}\subset \mathbb{C}$, $ψ_1$, $ψ_2$, and $ψ_3$ be three meromorphic functions in the unit disc $\mathbb{D}$, continuous on $ \partial{\mathbb{D}}:=\{z\in\mathbb{C}\,:\,|z|=1\}$, such that $ψ_i(z)\neqψ_j(z)$ $(1\leq i<j\leq 3)$ $\partial\mathbb{D}$. We prove that, if $ψ_1$, $ψ_2$, and $ψ_3$ share the function $f$ on $\mathbb{D}$, then $f$ is normal. Building upon this, we further establish an additional criterion for normal functions. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2509_16740 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | A Function-Sharing Criterion for Normal Functions Datt, Gopal Pal, Ritesh Trivedi, Ashish Kumar Complex Variables 30D45 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 $\mathbb{D}\subset \mathbb{C}$, $ψ_1$, $ψ_2$, and $ψ_3$ be three meromorphic functions in the unit disc $\mathbb{D}$, continuous on $ \partial{\mathbb{D}}:=\{z\in\mathbb{C}\,:\,|z|=1\}$, such that $ψ_i(z)\neqψ_j(z)$ $(1\leq i<j\leq 3)$ $\partial\mathbb{D}$. We prove that, if $ψ_1$, $ψ_2$, and $ψ_3$ share the function $f$ on $\mathbb{D}$, then $f$ is normal. Building upon this, we further establish an additional criterion for normal functions. |
| title | A Function-Sharing Criterion for Normal Functions |
| topic | Complex Variables 30D45 |
| url | https://arxiv.org/abs/2509.16740 |