Certain Nonlinear Differential Polynomials Sharing a Nonzero Polynomial with Finite Weight


  • Received : 2013.06.11
  • Accepted : 2013.10.14
  • Published : 2015.09.23


With the notion of weighted sharing of values we study the uniqueness of meromorphic functions when certain nonlinear differential polynomials share a nonzero polynomial. Our results improve some recent results including that of a present first author.


Meromorphic function;Weighted Sharing;Nonlinear differential polynomials


  1. A. Banerjee, Uniqueness of certain nonlinear differential polynomials sharing 1-points, Kyungpook Math. J., 51(2011), 43-58.
  2. A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci., 22(2005), 3587-3598.
  3. M. L. Fang, Uniqueness and value sharing of entire functions, Comput. Math. Appl., 44(2002), 823-831.
  4. C. Y. Fang and M. L. Fang, Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 44(2002), 607-617.
  5. W. K. Hayman, Picard values of meromorphic Functions and their derivatives, Ann. of Math., 70(1959), 9-42.
  6. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford (1964).
  7. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl., 46(2001), 241-253.
  8. I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sc., 28(2001), 83-91.
  9. I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), 38(2002), 119-128.
  10. I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., 26(2003), 95-100.
  11. J. D. Li, Uniqueness of meromorphic functions and differential polynomials, Int. J. Math. Math. Sci., 2011, Article ID 514218, 12 pages, doi:10.1155/2011/514218.
  12. W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic function concerning fixed points, Complex Var. Theory Appl., 49(2004), 793-806.
  13. H. Y. Xu, C. F. Yi and T. B. Cao, Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight, Ann. Polon. Math., 95(2009), 51-66.
  14. C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125(1972), 107-112.
  15. L. Yang, Value Distribution Theory, Springer-Verlag, Berlin, 1993.
  16. H. X. Yi and C. C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press, Beijing, 1995.
  17. J. L. Zhang, Uniqueness theorems for entire functions concerning fixed points, Comput. Math. Appl., 56(2008), 3079-3087.
  18. J. L. Zhang and L. Z. Yang, Some results related to a conjecture of R. Bruck, J. Inequal. Pure Appl. Math., 8(2007), Art. 18.