Abstract
Let {ie335-1} be a family of holomorphic functions in a domain D, k be a positive integer, a, b(≠0), c(≠0) and d be finite complex numbers. If, for each {ie335-2}, all zeros of f−d have multiplicity at least k, f( k )=a whenever f=0, and f=c whenever f( k )=b, then {ie335-3} is normal in D. This result extends the well-known normality criterion of Miranda and improves some results due to Chen-Fang, Pang and Xu. Some examples are provided to show that our result is sharp.
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