Dealing with a question of Lahiri [6] we study the uniqueness problem of meromorphic functions concerning two nonlinear differential polynomials sharing a small function. Our results will not only improve and supplement the results of Lin-Yi [16], Lahiri Sarkar [12] but also improve and supplement a very recent result of the first author [1].
@article{108095, author = {Abhijit Banerjee and Sonali Mukherjee}, title = {Nonlinear differential polynomials sharing~a~small~function}, journal = {Archivum Mathematicum}, volume = {044}, year = {2008}, pages = {41-56}, zbl = {1212.30113}, mrnumber = {2431230}, language = {en}, url = {http://dml.mathdoc.fr/item/108095} }
Banerjee, Abhijit; Mukherjee, Sonali. Nonlinear differential polynomials sharing a small function. Archivum Mathematicum, Tome 044 (2008) pp. 41-56. http://gdmltest.u-ga.fr/item/108095/
On uniqueness for nonlinear differential polynomials sharing the same $1$-point, Ann. Polon. Math. 89 (3) (2006), 259–272. (2006) | Article | MR 2262553 | Zbl 1104.30018
Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl. 44 (5–6) (2002), 607–617. (2002) | Article | MR 1925805 | Zbl 1035.30018
A unicity theorem for entire functions concerning differential polynomials, Indian J. Pure Appl. Math. 32 (9) (2001), 1343–1348. (2001) | MR 1875450 | Zbl 1005.30023
A unique range set for meromorphic functions with 11 elements, Complex Variables Theory Appl. 37 (9) (1998), 185–193. (1998) | Article | MR 1687880 | Zbl 1054.30519
Meromorphic Functions, The Clarendon Press, Oxford, 1964. (1964) | MR 0164038 | Zbl 0115.06203
Uniqueness of meromorphic functions when two linear differential polynomials share the same $1$-points, Ann. Polon. Math. 71 (2) (1999), 113–128. (1999) | MR 1703886 | Zbl 0938.30022
Value distribution of certain differential polynomials, Internat. J. Math. Math. Sci. 28 (2) (2001), 83–91. (2001) | Article | MR 1885054 | Zbl 0999.30023
Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206. (2001) | MR 1820218 | Zbl 0981.30023
Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory Appl. 46 (2001), 241–253. (2001) | Article | MR 1869738 | Zbl 1025.30027
Weighted sharing of two sets, Kyungpook Math. J. 46 (1) (2006), 79–87. (2006) | MR 2214802 | Zbl 1103.30017
Nonlinear differential polynomials sharing $1$-points, Bull. Korean Math. Soc. 43 (1) (2006), 161–168. (2006) | Article | MR 2204868 | Zbl 1183.30028
Nonlinear differential polynomials sharing $1$-points with weight two, Chinese J. Contemp. Math. 25 (3) (2004), 325–334. (2004) | MR 2159311 | Zbl 1069.30051
Uniqueness of meromorphic functions concerning weakly weighted sharing, Kodai Math. J. 29 (2006), 269–280. (2006) | Article | MR 2247436 | Zbl 1126.30018
Uniqueness of differential polynomials and a problem of Lahiri, Pure Appl. Math. 17 (2) (2001), 104–110, (in Chinese). (2001) | MR 1848848
Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math. 35 (2) (2004), 121–132. (2004) | MR 2040726 | Zbl 1056.30031
Uniqueness theorems for meromorphic functions concerning fixed points, Complex Variables Theory Appl. 49 (11) (2004), 793–806. (2004) | Article | MR 2097218 | Zbl 1067.30065
On the Nevanlinna characteristics of some meromorphic functions. Theory of Functions, Funct. Anal. Appl. 14 (1971), 83–87. (1971)
On deficiencies of differential polynomials II, Math. Z. 125 (1972), 107–112. (1972) | MR 0294642 | Zbl 0217.38402
Uniqueness of meromorphic functions and a question of C. C. Yang, Complex Variables Theory Appl. 14 (14) (1990), 169–176. (1990) | Article | MR 1048716 | Zbl 0701.30025
On characteristic function of a meromorphic function and its derivative, Indian J. Math. 33 (2) (1991), 119–133. (1991) | MR 1140875 | Zbl 0799.30018
Meromorphic functions that share one or two values, Complex Variables Theory Appl. 28 (1995), 1–11. (1995) | Article | Zbl 0841.30027