Meromorphic Functions with Weighted Sharing of One Set

  • Alzahary, Thamir C. (Department of Mathematics, Harbin Engineering University)
  • Received : 2005.10.12
  • Published : 2007.03.23

Abstract

In this article, we investigate the problem of uniqueness of meromorphic functions sharing one set and having deficient values, and obtain a result which improves some earlier results.

Keywords

References

  1. S. Bartels, Meromorphic functions sharing a set with 17 elements ignoring multiplicities, Complex variables, 39(1998), 85-92.
  2. M. L. Fang and X. H. Hua, Meromorphic functions that share one finite set CM, J. of Nanjing Univ. Math. Biquarterly, 1(1998), 15-22.
  3. G. Frank and M. Reinders, A unique range set for meromorphic functions with 11 elements, Complex Variables, 37(1998), 185-193. https://doi.org/10.1080/17476939808815132
  4. F. Groos, Factorization of meromorphic functions and some open problems, In Lecture Notes in Math., Springer, Berlin, 599(1977), 51-69
  5. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  6. I. Lahiri and A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J., 44(2004),575-584.
  7. P. Li and C. C. Yang, On the unique range sets of meromorphic functions, Pro. Amer. Math. Soc., 124(1996), 177-186. https://doi.org/10.1090/S0002-9939-96-03045-6
  8. P. Li and C. C. Yang, Some further results on the unique range sets of meromorphic functions, Kodai Math. J., 18(1995), 437-450. https://doi.org/10.2996/kmj/1138043482
  9. W. C. Lin and H. X. Yi, Uniqueness Theorems for meromorphic functions that share three sets, Complex Variables, 48(2003), 315-327. https://doi.org/10.1080/0278107021000037075
  10. C. C. Yang and H. X. Yi, Uniqueness theory of meromorphic functions. Kluwer Academic Publishers, Dordrecht-Bosten London 2003.
  11. X. Yan, Meromorphic functions sharing one finite set, Comp. and Math. with Appl., 45(2003), 1489-1495. https://doi.org/10.1016/S0898-1221(03)00132-9
  12. H. X. Yi, On a question of Gross, Science in China, Ser. A, 38(1)(1995), 8-16.