We deal with some uniqueness theorems of two transcendental meromorphic functions with their nonlinear differential polynomials sharing a small function. These results in this paper improve those given by C.-Y. Fang and M.-L. Fang (2002), by Lahiri and Pal (2006), and by Lin and Yi (2004).
L. Yang, Value Distribution Theory, Springer, Berlin, Germany, 1993.
View at: Zentralblatt MATH | MathSciNetR. Nevanlinna, Le Théorème de Picard-Borel et la Theéorie des Fonctions Méromorphes, Gauthier-Villars, Paris, France, 1929.
G. G. Gundersen, “Meromorphic functions that share three or four values,” The Journal of the London Mathematical Society, vol. 20, no. 3, pp. 457–466, 1979.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP. Li and C. C. Yang, “On two meromorphic functions that share pairs of small functions,” Complex Variables. Theory and Application, vol. 32, no. 2, pp. 177–190, 1997.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC.-Y. Fang and M.-L. Fang, “Uniqueness of meromorphic functions and differential polynomials,” Computers & Mathematics with Applications, vol. 44, no. 5-6, pp. 607–617, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetI. Lahiri and R. Pal, “Non-linear differential polynomials sharing 1-points,” Bulletin of the Korean Mathematical Society, vol. 43, no. 1, pp. 161–168, 2006.
View at: Google Scholar | MathSciNetM. Fang and H. Qiu, “Meromorphic functions that share fixed-points,” Journal of Mathematical Analysis and Applications, vol. 268, no. 2, pp. 426–439, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetW. Lin and H. X. Yi, “Uniqueness theorems for meromorphic functions concerning fixed-points,” Complex Variables. Theory and Application, vol. 49, no. 11, pp. 793–806, 2004.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetC. C. Yang, “On deficiencies of differential polynomials—II,” Mathematische Zeitschrift, vol. 125, no. 2, pp. 107–112, 1972.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, China, 1995.
G. Frank and M. Reinders, “A unique range set for meromorphic functions with elements,” Complex Variables. Theory and Application, vol. 37, no. 1–4, pp. 185–193, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. Fang and H. Guo, “On unique range sets for meromorphic or entire functions,” Acta Mathematica Sinica, vol. 14, no. 4, pp. 569–576, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet