- THE UNIQUENESS OF MEROMORPHIC FUNCTIONS WHOSE DIFFERENTIAL POLYNOMIALS SHARE SOME VALUES
- MENG, CHAO ; LI, XU ;
- Journal of applied mathematics & informatics, volume 33, issue 5_6, 2015, Pages 475~484
- DOI : 10.14317/jami.2015.475

Abstract

In this article, we deal with the uniqueness problems of meromorphic functions concerning differential polynomials and prove the following theorem. Let f and g be two nonconstant meromorphic functions, n ≥ 12 a positive integer. If f^{n}(f^{3} - 1)f′ and g^{n}(g^{3} - 1)g′ share (1, 2), f and g share ∞ IM, then f ≡ g. The results in this paper improve and generalize the results given by Meng (C. Meng, Uniqueness theorems for differential polynomials concerning fixed-point, Kyungpook Math. J. 48(2008), 25-35), I. Lahiri and R. Pal (I. Lahiri and R. Pal, Nonlinear differential polynomials sharing 1-points, Bull. Korean Math. Soc. 43(2006), 161-168), Meng (C. Meng, On unicity of meromorphic functions when two differential polynomials share one value, Hiroshima Math.J. 39(2009), 163-179).