A normality criterion for a family of meromorphic functions
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arXiv
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| Format: | Preprint |
| Published: |
2026
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| _version_ | 1866912963526393856 |
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| author | Mandal, Kuntal Pal, Bipul |
| author_facet | Mandal, Kuntal Pal, Bipul |
| contents | We consider a family $\mathscr{F}$ of meromorphic functions defined in a domain $D$, a holomorphic function $ψ$ and a homogeneous differential polynomial $ P[f] $ of degree $d$ with weight $w$. In this paper, we prove the normality of $\mathscr{F}$ under certain conditions such as $f\neq 0$, $P[f]\neq 0$ and all the zeros of the function $P[f] - ψ^d$ have multipicity at least $\displaystyle{\frac{w+1}{w-1}}$, for each $f \in \mathscr{F}$. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_12190 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A normality criterion for a family of meromorphic functions Mandal, Kuntal Pal, Bipul Complex Variables 30D35, 30D45 We consider a family $\mathscr{F}$ of meromorphic functions defined in a domain $D$, a holomorphic function $ψ$ and a homogeneous differential polynomial $ P[f] $ of degree $d$ with weight $w$. In this paper, we prove the normality of $\mathscr{F}$ under certain conditions such as $f\neq 0$, $P[f]\neq 0$ and all the zeros of the function $P[f] - ψ^d$ have multipicity at least $\displaystyle{\frac{w+1}{w-1}}$, for each $f \in \mathscr{F}$. |
| title | A normality criterion for a family of meromorphic functions |
| topic | Complex Variables 30D35, 30D45 |
| url | https://arxiv.org/abs/2603.12190 |