Uniqueness And Normality Of Meromorphic Functions With Sharing Values

We mainly study the uniqueness of meromorphic functions sharing one value with weight and the normal families of meromorphic functions sharing one function. This paper is divided into four chapters. The main contents are as follows:Chapter 1 gives the background of R.Nevanlinna theroy and the theroy of normal families.Chapter 2 investigates the uniqueness of differential polynomials of meromor-phic functions sharing one value with weight.We obtain one theroy which improve the result of X.M.Li.Theroy 1 Let f be a non-constant meromorphic function,let n, k be two positive integers and 2n>2k+5+(?), if fn and fn-1f(k) share (1,1), then f=f(k).Chapter 3 investigates the normality of meromorphic functions sharing func-tions.We obtain one theroy which improve the result of J.F.Chen.Theroy 2 Let F be a famliy of meromorphic function in a domain D, k be a positive integer, a(z) and b(z) be two holomorphic functions in D, moreover satisfied a(z)≠b(z),a(z)≠b(k) and a(z)(?)a'(z),if for each f∈F,f(z) has only zeros of multiplicity at least k, f(z) and f(k)(z) share a(z), when f(z)=b(z), there have f(k)(z)=b(z), then T is normal in D.Chapter 4 gives the normality of meromorphic functions sharing values.We obtain two theroies as follows.Theroy 3 Let F be a famliy of meromorphic function in a domain D, a≠0,6=0 be two finite complex numbers, if for each f∈F,there have f'fn=a(?) f=b, then F is normal in D. Theroy 4 Let F be a famliy of meromorphic function in a domain D,m≥2 and k be two positive integers, a≠0,b≠0 be two finite complex numbers, if for each f∈F,f(z) has only zeros of multiplicity at least k+1, moreover satisfied fmf(k)=a(?)f=b, then F is normal in D.