Kyungpook Mathematical Journal

  • 제49권1호
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  • Pages.15-29
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  • 2009
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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Uniqueness of Meromorphic Functions That Share Three Sets

  • Banerjee, Abhijit (Department of Mathematics, Kalyani Government Engineering College)
  • 투고 : 2007.03.22
  • 발행 : 2009.03.31
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초록

Dealing with a question of gross, we prove some uniqueness theorems concerning meromorphic functions with the notion of weighted sharing of sets. Our results will not only improve and supplement respectively two results of Lahiri-Banerjee [9] and Qiu and Fang [13] but also improve a very recent result of the present author [1].

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참고문헌

  1. A. Banerjee, On a question of Gross, J. Math. Anal. Appl., 327(2007), 1273-1283. https://doi.org/10.1016/j.jmaa.2006.04.078
  2. M. Fang and W. Xu, A note on a problem of Gross, Chinese J. Contemporary Math., 18(1997), 395-402.
  3. F. Gross, Factorization of meromorphic functions and some open problems, Proc. Conf. Univ. Kentucky, Leixngton, Ky(1976)
  4. F. Gross, Factorization of meromorphic functions and some open problems, Lecture Notes in Math., 599(1977), 51-69, Springer(Berlin). https://doi.org/10.1007/BFb0096825
  5. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  6. I. Lahiri, Value distribution of certain differential polynomials. Int. J. Math. Math. Sci., 28(2001), 83-91. https://doi.org/10.1155/S0161171201011036
  7. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J., 161(2001), 193-206. https://doi.org/10.1017/S0027763000027215
  8. I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46(2001), 241-253. https://doi.org/10.1080/17476930108815411
  9. I. Lahiri, On a question of Hong Xun Yi, Arch. Math. (Brno), 38(2002), 119-128.
  10. I. Lahiri and A. Banerjee, Uniqueness of meromorphic functions with deficient poles, Kyungpook Math. J., 44(2004), 575-584.
  11. I. Lahiri and A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J., 46(2006), 79-87.
  12. I. Lahiri and S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J., 26(2003), 95-100. https://doi.org/10.2996/kmj/1050496651
  13. W. C. Lin and H. X. Yi, Uniqueness theorems for meromorphic functions that share three sets, Complex Var. Theory Appl. 48(2003), 315-327. https://doi.org/10.1080/0278107021000037075
  14. H. Qiu and M. Fang, A unicity theorem for meromorphic functions, Bull. Malaysian Math. Sci. Soc., 25(2002) 31-38.
  15. C. C. Yang, On deficiencies of differential polynomials II, Math. Z., 125(1972), 107-112. https://doi.org/10.1007/BF01110921
  16. H. X. Yi, Uniqueness of meromorphic functions and a question of Gross, [J] Science in China (Ser A), 37(1994), 802-813.
  17. H. X. Yi, Meromorphic functions that share one or two values, Complex Var. Theory Appl., 28(1995), 1-11. https://doi.org/10.1080/17476939508814832
  18. H. X. Yi, Meromorphic functions that share one or two values II, Kodai Math. J., 22(1999), 264-272. https://doi.org/10.2996/kmj/1138044046
  19. H. X. Yi and W. C. Lin, Uniqueness theorems concerning a question of Gross, Proc. Japan Acad., Ser.A, 80(2004), 136-140. https://doi.org/10.3792/pjaa.80.136

피인용 문헌

  1. Uniqueness and set sharing of derivatives of meromorphic functions vol.61, pp.2, 2011, https://doi.org/10.2478/s12175-011-0005-6