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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 is normal in a domain D, if (i) for every pair of functions f and g in , 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, where a and b are two finite complex numbers such that a0, nk+3 and k2 are two positive integers. An example shows that the condition (ii) in our results is best possible.
MSC:
30D45Bloch functions, normal functions, normal families
30D35Distribution of values (one complex variable); Nevanlinna theory