Journals / Turkish Journal of Mathematics / 2009 / Cilt: 33 - Sayı: 4
Uniqueness for meromorphic functions and differential polynomials
- Pages
- 331–340
- DOI
- —
Abstract
In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials and prove the following result: Let f and g be two transcendental meromorphic functions, a be a meromorphic function such that T(r,a)=o(T(r,f)+T(r,g)) and a \not\equiv 0,\infty. Let a be a nonzero constant. Suppose that m,n are positive integers such that n>m+10. If Yf' and Yg' share ``(0,2)", then (i) if m\geq 2, then f(z)\equiv g(z); (ii) if m=1, either f(z)\equiv g(z) or f and g satisfy the algebraic equation R(f,g)\equiv 0, where R(\varpi1,\varpi2)=(n+1)(\varpi1n+2-\varpi2n+2)-(n+2)(\varpi1n+1 -\varpi2n+1). The results in this paper improve the results of Xiong-Lin-Mori 14 and the author 12.
Özet
In this article, we deal with the uniqueness problems on meromorphic functions concerning differential polynomials and prove the following result: Let f and g be two transcendental meromorphic functions, a be a meromorphic function such that T(r,a)=o(T(r,f)+T(r,g)) and a \not\equiv 0,\infty. Let a be a nonzero constant. Suppose that m,n are positive integers such that n>m+10. If Yf' and Yg' share ``(0,2)", then (i) if m\geq 2, then f(z)\equiv g(z); (ii) if m=1, either f(z)\equiv g(z) or f and g satisfy the algebraic equation R(f,g)\equiv 0, where R(\varpi1,\varpi2)=(n+1)(\varpi1n+2-\varpi2n+2)-(n+2)(\varpi1n+1 -\varpi2n+1). The results in this paper improve the results of Xiong-Lin-Mori 14 and the author 12.