On Some Results Of Meromorphic Functions And Their Derivatives On Shared Values

In this thesis,base on Nevanlinna theory,the 1CM+3IM problem and the uniqueness of meromorphic functions with their derivatives sharing one valve are further studied.On the research of 1CM+2IM problem,we mainly prove the following conclusion:Let f(z)and g(z)are non-constant entire functions with finite order,c be a complex number dififferent from 0,1,∞.If f(z)and g(z)sharing 0,1,c IM,and(?)η∈(π,2π]such that in the following two sets{r|r>0,且mes{θ|θ∈[0,2π],|f(reiθ)|≥|g(reiθ)|}>η},{r|r>0,且mes{θ|θ∈[0,2π],|g(reiθ)|≥|f(reiθ)|}>η},at least one of them has infinity logarithmic measure,then f(z)≡g(z).In the study of the uniqueness of meromorphic functions and their derivatives sharing finite value,the following conclusion are obtained:Let f(z)be a transcendental meromorphic function,k(>1)be an inte ger.if f(z)and f’(z)share the value 1 IM,f’(z)and f(k)(z)share the va lue 1 CM,and (?),then f(z)≡f(k)(z).