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RESULTS ON MEROMORPHIC FUNCTIONS SHARING THREE VALUES CM IN SOME ANGULAR DOMAINS

Li, Xiao-Min;Liu, Xue-Feng;Yi, Hong-Xun

  • Received : 2015.07.30
  • Published : 2016.07.31

Abstract

We study the uniqueness question of transcendental meromorphic functions that share three values CM in some angular domains instead of the whole complex plane. The results in this paper extend the corresponding results in Zheng [13, 14] and Yi [12]. Some examples are given to show that the results in this paper, in a sense, are the best possible.

Keywords

Nevanlinna theory;meromorphic functionsm;shared values;uniqueness theorems

References

  1. A. Baernstein, Proof of Edrei's spread conjecture, Proc. London Math. Soc. 26 (1973), 418-434.
  2. I. N. Baker, Sets of non-normality in iteration theory, J. London Math. Soc. 40 (1965), 499-502.
  3. W. Bergweiler, Iteration of meromorphic functions, Bull. Amer.Math. Soc. (N.S.) 29 (1993), no. 2151-188.
  4. A. Edrei, Meromorphic functions with three radially distributed values, Trans. Amer. Math. Soc. 78 (1955), 276-293. https://doi.org/10.1090/S0002-9947-1955-0067982-9
  5. A. Edrei, Sums of deficiencies of meromorphic functions, J. Analyse Math. 14 (1965), 79-107. https://doi.org/10.1007/BF02806380
  6. A. A. Goldberg and I. V. Ostrovskii, Value Distribution of Meromorphic Functions, 2nd Edition (Translations of Mathematical Monographs), Vol. 236, American Mathematical Society, Rhode Island, Providence, 2008.
  7. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  8. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin/ New York, 1993.
  9. R. Nevanlinna, Le theoreme de Picard-Borel et la theorie des fonctions mromorphes, Gauthier-Villars, Paris, 1929.
  10. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.
  11. L. Yang, Borel directions of meromorphic functions in an angular domain, Sci. Sinica (1979), 149-164.
  12. H. X. Yi, Unicity theorems for meromorphic functions that share three values, Kodai Math. J. 18 (1995), no. 2, 300-314. https://doi.org/10.2996/kmj/1138043427
  13. J. H. Zheng, On Uniqueness of meromorphic functions with shared values in one angular domain, Complex Var. Theory Appl. 48 (2003), no. 9, 777-785.
  14. J. H. Zheng, On uniqueness of meromorphic functions with shared values in some angular domains, Canad. Math. Bull. 47 (2004), no. 1, 152-160. https://doi.org/10.4153/CMB-2004-016-1

Acknowledgement

Supported by : NSFC, NSF of Shandong Province