# UNIQUENESS OF ENTIRE FUNCTIONS AND DIFFERENTIAL POLYNOMIALS

• Xu, Junfeng (DEPARTMENT OF MATHEMATICS SHANDONG UNIVERSITY) ;
• Yi, Hongxun (DEPARTMENT OF MATHEMATICS SHANDONG UNIVERSITY)
• Published : 2007.11.30
• 115 8

#### Abstract

In this paper, we study the uniqueness of entire functions and prove the following result: Let f and g be two nonconstant entire functions, n, m be positive integers. If $f^n(f^m-1)f#\;and\;g^n(g^m-1)g#$ share 1 IM and n>4m+11, then $f{\equiv}g$. The result improves the result of Fang-Fang.

#### Keywords

uniqueness;entire function;sharing values

#### References

1. C. Y. Fang and M. L. Fang, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl. 44 (2002), no. 5-6, 607-617 https://doi.org/10.1016/S0898-1221(02)00175-X
2. W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs, The Clarendon Press, Oxford, 1964
3. W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic function, Indian J. Pure Appl. Math. 35 (2004), no. 2, 121-132
4. H. L. Qiu and M. L. Fang, On the uniqueness of entire functions, Bull Korean Math. Soc. 41 (2004), no. 1, 109-116 https://doi.org/10.4134/BKMS.2004.41.1.109
5. C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003
6. L. Yang, Value distribution theory, Translated and revised from the 1982 Chinese origi- nal. Springer-Verlag, Berlin; Science Press, Beijing, 1993
7. H. X. Yi, A question of Gross and the uniqueness of entire functions, Nagoya Math. J. 138 (1995), 169-177 https://doi.org/10.1017/S0027763000005225
8. H. X. Yi, Meromorphic functions that share one or two values II, Kodai Math. J. 22(1999), no. 2, 264-272 https://doi.org/10.2996/kmj/1138044046
9. F. Gross, Factorization of meromorphic functions and some open problems, Complex analysis (Proc. Conf., Univ. Kentucky, Lexington, Ky., 1976), pp. 51-67. Lecture Notes in Math., Vol. 599, Springer, Berlin, 1977 https://doi.org/10.1007/BFb0096825
10. H. X. Yi, Meromorphic functions that share one or two values, Complex Variables Theory Appl. 28 (1995), no. 1, 1-11 https://doi.org/10.1080/17476939508814833

#### Cited by

1. Some results on zeros and uniqueness of difference-differential polynomials vol.27, pp.1, 2012, https://doi.org/10.1007/s11766-012-2795-x
2. Generalization of Uniqueness Theorems for Entire and Meromorphic Functions vol.05, pp.08, 2014, https://doi.org/10.4236/am.2014.58118
3. On the Uniqueness Results and Value Distribution of Meromorphic Mappings vol.5, pp.3, 2017, https://doi.org/10.3390/math5030042
4. Some Uniqueness Results of Q-Shift Difference Polynomials Involving Sharing Functions vol.08, pp.08, 2017, https://doi.org/10.4236/am.2017.88084
5. Value Sharing Results forq-Shifts Difference Polynomials vol.2013, 2013, https://doi.org/10.1155/2013/152069
6. Zeros and shared one value of q-shift difference polynomials vol.50, pp.2, 2015, https://doi.org/10.3103/S1068362315020028
7. VALUE DISTRIBUTION AND UNIQUENESS ON q-DIFFERENCES OF MEROMORPHIC FUNCTIONS vol.50, pp.4, 2013, https://doi.org/10.4134/BKMS.2013.50.4.1157
8. Zeros and Uniqueness of Difference Polynomials of Meromorphic Functions vol.53, pp.4, 2013, https://doi.org/10.5666/KMJ.2013.53.4.541
9. Value Distributions and Uniqueness of Difference Polynomials vol.2011, 2011, https://doi.org/10.1155/2011/234215
10. Results on Uniqueness of Entire Functions Related to Difference Polynomial vol.39, pp.2, 2016, https://doi.org/10.1007/s40840-015-0122-4
11. WEIGHTED SHARING AND UNIQUENESS OF ENTIRE OR MEROMORPHIC FUNCTIONS vol.52, pp.1, 2015, https://doi.org/10.4134/BKMS.2015.52.1.013