Yuling Xia
Abstract
In this paper,the normality of a family of meromorphic functions related to shared a value has been researched,and the following result is proved: Let F be a family of mermorphic functions on the unit disc Δ,and k be a positive integer.If all zeros of f-a are of multiplicity at least k,and f(z)=a■f(k)(z)=a■f(k+1)(z)=a for every f∈F,then F is normal on Δ.
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In this paper,the normality of a family of meromorphic functions related to shared a value has been researched,and the following result is proved: Let F be a family of mermorphic functions on the unit disc Δ,and k be a positive integer.If all zeros of f-a are of multiplicity at least k,and f(z)=a■f(k)(z)=a■f(k+1)(z)=a for every f∈F,then F is normal on Δ.
Key concepts: Normal family, Meromorphic function, Multiplicity (mathematics), Normality, Combinatorics, Mathematics, Integer (computer science), Value (mathematics)