DOI QR코드

DOI QR Code

ON UNIQUENESS OF MEROMORPHIC FUNCTIONS WHEN TWO DIFFERENTIAL MONOMIALS SHARE ONE VALUE

  • Banerjee, Abhijit (DEPARTMENT OF MATHEMATICS KALYANI GOVERNMENT ENGINEERING COLLEGE)
  • Published : 2007.11.30

Abstract

We prove four theorems on the uniqueness of non linear differential polynomials sharing one value which improve a result of Yang and Hua, and supplements some results of Lahiri, Xu and Qiu and Banerjee.

Keywords

uniqueness;meromorphic function;non-linear differential polynomial;shared value

References

  1. A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci. (2005), no. 22, 3587-3598 https://doi.org/10.1155/IJMMS.2005.3587
  2. W. K. Hayman, Meromorphic functions, Oxford Mathematical Monographs Clarendon Press, Oxford 1964
  3. I. Lahiri, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci. 28 (2001), no. 2, 83-91 https://doi.org/10.1155/S0161171201011036
  4. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206 https://doi.org/10.1017/S0027763000027215
  5. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Variables Theory Appl. 46 (2001), no. 3, 241-253 https://doi.org/10.1080/17476930108815411
  6. I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J. 46 (2006), no. 1, 79-87
  7. I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J. 26 (2003), no. 1, 95-100 https://doi.org/10.2996/kmj/1050496651
  8. A. Z. Mohon'ko, The Nevanlinna characteristics of certain meromorphic functions, Teor. FunkciiFunkcional. Anal. i Prilozen. No. 14 (1971), 83-87
  9. E. Mues and M. Reinders, Meromorphic functions sharing one value and unique range sets, Kodai Math. J. 18 (1995), no. 3, 515-522 https://doi.org/10.2996/kmj/1138043489
  10. C. C. Yang, On deficiencies of differential polynomials. II, Math. Z. 125 (1972), 107-112 https://doi.org/10.1007/BF01110921
  11. C. C. Yang and X. Hua, Uniqueness and value-sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), no. 2, 395-406
  12. H. X. Yi, Uniqueness of meromorphic functions and a question of C. C. Yang, Complex Variables Theory Appl. 14 (1990), no. 1-4, 169-176 https://doi.org/10.1080/17476939008814415
  13. 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
  14. H. X. Yi, Some further results on uniqueness of meromorphic functions, Complex Variables Theory Appl. 38 (1999), no. 4, 375-385 https://doi.org/10.1080/17476939908815175
  15. Y. Xu and H. Qiu, Entire functions sharing one value IM, Indian J. Pure Appl. Math. 31 (2000), no. 7, 849-855
  16. H. X. Yi, On characteristic function of a meromorphic function and its derivative, Indian J. Math. 33 (1991), no. 2, 119-133

Cited by

  1. Uniqueness of meromorphic functions whose nonlinear differential polynomials share a polynomial vol.9, pp.4, 2016, https://doi.org/10.1007/s40574-016-0062-4
  2. Entire Functions and Their Derivatives Share Two Finite Sets vol.49, pp.3, 2009, https://doi.org/10.5666/KMJ.2009.49.3.473