Uniqueness of Meromorphic Functions Sharing a Rational Function

In this paper,we study the uniqueness of two meromorphic functions fnf′,gng′ weakly weighted sharing a rational function and the following result is proved:let p(z),q(z) be two co-prime polynomials of n1,n2 respectively,let f,g be two non-constant transcendental meromorphic functions.If fnf′ and gng′ share (p(z)q(z),m) and(i) when 2≤m≤∞;n≥max{11,2n1+4n2+3};(ii) when m=1,n≥max{13,2n1+4n2+3};(iii) when m=0,n≥max{23,2n1+4n2+3},then f=c1Q(z)exp(α(z)),g=c2Q-1(z)exp(-α(z)),where c1,c2 are two constants,Q(z) is a rational function,and α(z) is a non-constant polynomial satisfying(c1c2)n+1(Q′(z)/Q(z)+α′(z))2≡(p(z)/q(z))2 or f=tg for a constant t satisfying tn+1=1.