## Some normality criteria of function families concerning shared values.(English)Zbl 1273.30023

Summary: We study the normality of families of meromorphic functions related to shared values. We mainly consider whether a family of meromorphic functions $$\mathcal F$$ is normal in a domain $$D$$, if (i) for every pair of functions $$f$$ and $$g$$ in $$\mathcal F$$, $$f^{(k)} - af^{n}$$ and $$g^{(k)} - ag^{n}$$ share the value $$b$$, and (ii) $$f$$ has no zero of multiplicity less than $$k$$ in $$D$$ for every function $$f \in \mathcal F$$, where $$a$$ and $$b$$ are two finite complex numbers such that $$a \neq 0$$, $$n\geq k+3$$ and $$k \geq 2$$ are two positive integers. An example shows that the condition (ii) in our results is best possible.

### MSC:

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

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