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On Normal Families of Meromorphic Functions

LAN Fu-xiang,LI Jiang-taoCollege of Mathematic and Physics,Chongqing University,Chongqing 400030,China  
Let F be a family of meromorphic functions in a domain D,a(z)be a non-vanishing analytic function in D.Let k be a positive integer such that k≥3,and A,B be two positive real numbers.a0(z),a1(z),…,ak-1(z) are analytic functions in the domain D.If for every function f∈F,f has only zeros of multiplicity at least k and satisfies the following conditions:(1°) if f(k)(z)+ak-1(z)f(k-1)(z)+…a1(z)f′(z)+a0(z)f(z)=a(z),then |f(z)|≥A(z∈D);(2°) If f(z)=0 then,0f(k)(z)≤B(z∈D),Then F is normal in D.
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