Uniqueness And Normality Of Meromorphic Functinons Concerning Differential Polynomials

It's an important topic in the theory of normal family and uniqueness of meromorphic functions that considering differential polynomials. This paper mainly studies the normality of a family of meromorphic functions and the uniqueness problem of two meromorphic functions whose differential polynomials share the same 1-points. Through the analysis, the author obtains one related normality criteria and two uniqueness theorems of differential polynomials sharing 1-points.In the end,I study the uniqueness of meromorphic functions which have unique range set and prove the following theorem :Let S={z∶zⁿ+az^n-1+b=0}, where n is a positive integer and a ,b are two nonzero constants such that zⁿ+az^n-1+b=0 has no multiple root. Let f and g be two nonconstant meromorphicfunctions and (?)(∞;f)+(?)(∞;g)>t. If E_f(S,2)=E_g(S,2),E_f({∞})=E_g({∞}),then f≡g.wherei) n≥8 t=4/n-1 or ii)n≥7 t=4/n-3. This result extends some results of YiHong- Xun and I.Lahiri.