A normality Criterion for a Family of Meromorphic Functions
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arXiv
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| Hauptverfasser: | , |
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| Format: | Preprint |
| Veröffentlicht: |
2019
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| _version_ | 1866909111079141376 |
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| author | Datt, Gopal Kumar, Sanjay |
| author_facet | Datt, Gopal Kumar, Sanjay |
| contents | Schwick, in [6], states that let $\mathcal{F}$ be a family of meromorphic functions on a domain $D$ and if for each $f\in\mathcal{F}$, $(f^n)^{(k)}\neq 1$, for $z\in D$, where $n, k$ are positive integers such that $n\geq k+3$, then $\mathcal{F}$ is a normal family in $D$. In this paper, we investigate the opposite view that if for each $f\in\mathcal{F}$, $(f^n)^{(k)}(z)-ψ(z)$ has zeros in $D$, where $ψ(z)$ is a holomorphic function in $D$, then what can be said about the normality of the family $\mathcal{F}$? |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_1909_00139 |
| institution | arXiv |
| publishDate | 2019 |
| record_format | arxiv |
| spellingShingle | A normality Criterion for a Family of Meromorphic Functions Datt, Gopal Kumar, Sanjay Complex Variables 30D45 Schwick, in [6], states that let $\mathcal{F}$ be a family of meromorphic functions on a domain $D$ and if for each $f\in\mathcal{F}$, $(f^n)^{(k)}\neq 1$, for $z\in D$, where $n, k$ are positive integers such that $n\geq k+3$, then $\mathcal{F}$ is a normal family in $D$. In this paper, we investigate the opposite view that if for each $f\in\mathcal{F}$, $(f^n)^{(k)}(z)-ψ(z)$ has zeros in $D$, where $ψ(z)$ is a holomorphic function in $D$, then what can be said about the normality of the family $\mathcal{F}$? |
| title | A normality Criterion for a Family of Meromorphic Functions |
| topic | Complex Variables 30D45 |
| url | https://arxiv.org/abs/1909.00139 |