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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 $ℱ$ is normal in a domain $D$, if (i) for every pair of functions $f$ and $g$ in $ℱ$, ${f}^{\left(k\right)}-a{f}^{n}$ and ${g}^{\left(k\right)}-a{g}^{n}$ share the value $b$, and (ii) $f$ has no zero of multiplicity less than $k$ in $D$ for every function $f\in ℱ$, where $a$ and $b$ are two finite complex numbers such that $a\ne 0$, $n\ge k+3$ and $k\ge 2$ are two positive integers. An example shows that the condition (ii) in our results is best possible.
##### MSC:
 30D45 Bloch functions, normal functions, normal families 30D35 Distribution of values (one complex variable); Nevanlinna theory