Youming Wang
Abstract
Let F be a family of meromorphic functions in a domain D■C,let k≥2 be a positive integer,and a,b,c,d be four finite complex numbers such that c≠0,d≠a,c≠b.If for every f∈F,all zeros of f-a have multiplicity at least k,and f(k)=b if and only if f=a,and f =d whenever f(k)=c,then F is normal in D.
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Let F be a family of meromorphic functions in a domain D■C,let k≥2 be a positive integer,and a,b,c,d be four finite complex numbers such that c≠0,d≠a,c≠b.If for every f∈F,all zeros of f-a have multiplicity at least k,and f(k)=b if and only if f=a,and f =d whenever f(k)=c,then F is normal in D.
Key concepts: Meromorphic function, Multiplicity (mathematics), Normality, Normal family, Mathematics, Combinatorics, Integer (computer science), Domain (mathematical analysis)