Research ArticleOpen AccessGoogle Scholar indexed
Generalization of Uniqueness Theorems for Entire and Meromorphic Functions
Department of Mathematics, Central College Campus, Bangalore University, Bangalore, India
P. G. Department of Mathematics, M. E. S. College, Bangalore, India
- 1 Department of Mathematics, Central College Campus, Bangalore University, Bangalore, India
- 2 P. G. Department of Mathematics, M. E. S. College, Bangalore, India
Applied Mathematics·Volume 05 (2014)·Pages 1267–1274·Published 24 April 2014·DOI10.4236/am.2014.58118
Copy link · social · email
Abstract
In this paper, we deal with the uniqueness problems on entire and meromorphic functions con- cerning differential polynomials that share fixed-points. Moreover, we generalise and improve some results of Weichuan Lin, Hongxun Yi, Meng Chao, C. Y. Fang, M. L. Fang and Junfeng xu.
KeywordsNevanlinna TheoryUniquenessEntire FunctionsMeromorphic FunctionsDifferential PolynomialsFixed Points
- Hayman, W.K. (1964) Meromorphic Functions. Clarendon Press, Oxford.
- Yang, C.C. and Hua, X.H. (1997) Uniqueness and Value-Sharing of Meromorphic Functions. Annales Academia Scientiarum Fennica Mathematica, 22, 395-406.
- Fang, M.L. and Hong, W. (2001) A Unicity Theorem for Entire Functions Concerning Differential Polynomials, Indian. Journal of Pure and Applied Mathematics, 32, 1343-1348.
- Lin, W.C. and Yi, H.X. (2004) Uniqueness Theorem for Meromorphic Functions Concerning Fixed Points. Complex Variables, Theory and Application, 49, 793-806.
- Chao, M. (2008) Uniqueness Theorems for Differential Polynomials Concerning Fixed Points. Kyungpook Mathematical Journal, 48, 25-35. http://dx.doi.org/10.5666/KMJ.2008.48.1.025
- Fang, C.Y. and Fang, M.L. (2002) Uniqueness of Meromorphic Functions and Differential Polynomials. Computers & Mathematics with Applications, 44, 607-617. http://dx.doi.org/10.1016/S0898-1221(02)00175-X
- Lin, W.C. and Yi, H.X. (2004) Uniqueness Theorems for Meromorphic Functions. Indian Journal of Pure and Applied Mathematics, 35, 121-132.
- Qiu, H.L. and Fang, M.L. (2004) On the Uniqueness of Entire Functions. Bulletin of the Korean Mathematical Society, 41, 109-116. http://dx.doi.org/10.4134/BKMS.2004.41.1.109
- Yang, C.C. and Yi, H.X. (2003) Uniqueness Theory of Meromorphic Functions. Kluwer Academic Publishers, London.
- Zhang, Q.C. (2005) Meromorphic Functions That Share One Small Functions with Its Derivatives. Journal of Inequalities in Pure and Applied Mathematics, 6, Article ID: 116.
- Xu, J.F. and Yi, H.X. (2007) Uniqueness of Entire Functions and Differential Polynomials. Bulletin of the Korean Mathematical Society, 44, 623-629. http://dx.doi.org/10.4134/BKMS.2007.44.4.623
- Yi, H.X. (1999) Meromorphic Functions That Share One or Two Values II. Kodai Mathematical Journal, 22, 264-272. http://dx.doi.org/10.2996/kmj/1138044046
- Yi, H.X. (1995) Meromorphic functions That Share One or Two Values. Complex Variables, Theory and Application, 28, 1-11.
- Frank, G. and Reiders, M. (1998) A Unique Range Set for Meromorphic Functions with 11 Elements. Complex Variables, Theory and Application, 37, 185-193.