On an Open Problem of Xiao-Bin Zhang and Jun-Feng Xu



The purpose of the paper is to study the uniqueness of meromorphic functions sharing a nonzero polynomial. The results of the paper improve and generalize the recent results due to X. B. Zhang and J. F. Xu [19]. We also solve an open problem as posed in the last section of [19].

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  • [1] A. Banerjee, Meromorphic functions sharing one value, Int. J. Math. Math. Sci. 22 (2005), 3587-3598.

  • [2] A. Banerjee, Uniqueness of certain nonlinear differential polynomials sharing 1-points, Kyungpook Math. J. 51 (2011), 43-58.

  • [3] M. L. Fang, H. L. Qiu, Meromorphic functions that share fixed points, J. Math. Anal. Appl. 268 (2002), 426-439.

  • [4] G. Frank, Eine Vermutung Von Hayman über Nullslellen meromorphic Funktion, Math. Z. 149 (1976), 29-36.

  • [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, Value distribution of certain differential polynomials, Int. J. Math. Math. Sci. 28 (2001), 83-91.

  • [8] I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193-206.

  • [9] I. Lahiri, Weighted value sharing and uniqueness of meromorphic functions, Complex Var. Theory Appl. 46 (2001), 241-253.

  • [10] I. Lahiri, A. Banerjee, Weighted sharing of two sets, Kyungpook Math. J. 46 (2006), 79-87.

  • [11] I. Lahiri, S. Dewan, Value distribution of the product of a meromorphic function and its derivative, Kodai Math. J. 26 (2003), 95-100.

  • [12] J. F. Xu, F. Lu, H. X. Yi, Fixed points and uniqueness of meromorphic functions, Comput. Math. Appl. 59 (2010), 9-17.

  • [13] C. C. Yang, On deficiencies of differential polynomials II, Math. Z. 125 (1972), 107-112.

  • [14] C. C. Yang, X. H. Hua, Uniqueness and value sharing of meromorphic functions, Ann. Acad. Sci. Fenn. Math. 22 (1997), 395-406.

  • [15] C. C. Yang, H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.

  • [16] H. X. Yi, Meromorphic functions that share three sets, Kodai Math. J. 20 (1997), 22-32.

  • [17] H. X. Yi, Meromorphic functions that share one or two values II, Kodai Math. J. 22 (1999), 264-272.

  • [18] Q. C. Zhang, Meromorphic function that shares one small function with its derivative, J. Inequal. Pure Appl. Math. 6(4) (2005), Art. 116 [online: http://jipam.vu.edu.au/].

  • [19] X. B. Zhang, J. F. Xu, Uniqueness of meromorphic functions sharing a small function and its applications, Comput. Math. Appl. 61 (2011), 722-730.


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