## Some normality criteria of meromorphic functions.(English)Zbl 1152.30033

Relations between the normality of a family $${\mathcal F}$$ of meromorphic functions in a domain $$D$$ and sharing values of functions in $${\mathcal F}$$ is studied. It is proved the following
Theorem 1. Let $${\mathcal F}$$ be a family of meromorphic functions in $$D$$ such that all zeros and poles of $$f\in {\mathcal F}$$ have multiplicities at least 3. If for each pair of functions $$f$$ and $$g$$ in $${\mathcal F}$$, $$f^{\prime}$$ and $$g^{\prime}$$ share a non-zero value $$b$$ in $$D$$, then $${\mathcal F}$$ is a normal family in $$D$$.
As an application of Theorem 1. the following result is proved.
Theorem 2. Let $${\mathcal F}$$ be a family of meromorphic functions in $$D$$, and $$n$$ be a positive integer. If $$n \geq 2$$ and for each pair of functions $$f$$ and $$g$$ in $${\mathcal F}$$, $$f^{\prime\prime} f^{\prime}$$ and $$g^{\prime\prime} g^{\prime}$$ share a non-zero value $$b$$ in $$D$$, then $${\mathcal F}$$ is a normal family in $$D$$.

### MSC:

 30D35 Value distribution of meromorphic functions of one complex variable, Nevanlinna theory 30D45 Normal functions of one complex variable, normal families

### Keywords:

normal family; sharing values
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### References:

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