Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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THE UNIQUENESS THEOREMS OF MEROMORPHIC FUNCTIONS SHARING THREE VALUES AND ONE PAIR OF POLYNOMIALS

  • Li, Xiao-Min (DEPARTMENT OF MATHEMATICS OCEAN UNIVERSITY OF CHINA, DEPARTMENT OF PHYSICS AND MATHEMATICS UNIVERSITY OF EASTERN FINLAND) ;
  • Yi, Hong-Xun (DEPARTMENT OF MATHEMATICS SHANDONG UNIVERSITY)
  • Received : 2009.02.11
  • Published : 2010.07.31
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Abstract

In this paper, we deal with a uniqueness theorem of two nonconstant meromorphic functions that share three values and one pair of polynomials. The results in this paper improve those given by G. G. Gundersen, G. Brosch and other authors.

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References

  1. A. H. H. Al-Khaladi, Unicity theorems for meromorphic functions, Kodai Math. J. 23 (2000), no. 1, 27–34. https://doi.org/10.2996/kmj/1138044154
  2. T. C. Alzahary, Weighted sharing three values and Brosch’s theorem, J. Math. Anal. Appl. 323 (2006), no. 1, 8–25. https://doi.org/10.1016/j.jmaa.2005.10.009
  3. T. C. Alzahary and H. X. Yi, Weighted sharing three values and uniqueness of meromorphic functions, J. Math. Anal. Appl. 295 (2004), no. 1, 247–257. https://doi.org/10.1016/j.jmaa.2004.03.040
  4. T. C. Alzahary and H. X. Yi, Meromorphic functions that weighted sharing three values and one pair, Kodai Math. J. 29 (2006), no. 1, 13–30. https://doi.org/10.2996/kmj/1143122383
  5. G. Brosch, Eindeutigkeitssatze fur meromorphe Funktionen, Thesis, Technical University of Aachen, 1989.
  6. F. Gross, On the distribution of values of meromorphic functions, Trans. Amer. Math. Soc. 131 (1968), 199–214. https://doi.org/10.1090/S0002-9947-1968-0220938-4
  7. G. G. Gundersen, Meromorphic functions that share three or four values, J. London Math. Soc. (2) 20 (1979), no. 3, 457–466. https://doi.org/10.1112/jlms/s2-20.3.457
  8. W. K. Hayman, Meromorphic Functions, The Clarendon Press, Oxford, 1964.
  9. I. Lahiri, Weighted sharing and uniqueness of meromorphic functions, Nagoya Math. J. 161 (2001), 193–206.
  10. I. Lahiri, Weighted sharing of three values and uniqueness of meromorphic functions, Kodai Math. J. 24 (2001), no. 3, 421–435. https://doi.org/10.2996/kmj/1106168813
  11. I. Lahiri and P. Sahoo, On a result of G. Brosch, J. Math. Anal. Appl. 331 (2007), no. 1, 532–546. https://doi.org/10.1016/j.jmaa.2006.09.009
  12. X. M. Li and H. X. Yi, The uniqueness theorems of meromorphic functions sharing three values and one pair of values, J. Math. Anal. Appl. 339 (2008), no. 1, 609–621. https://doi.org/10.1016/j.jmaa.2007.07.020
  13. P. Li and C. C. Yang, On two meromorphic functions that share pairs of small functions, Complex Variables Theory Appl. 32 (1997), no. 2, 177–190. https://doi.org/10.1080/17476939708814988
  14. X. M. Li and H. X. Yi, Weighted sharing of meromorphic functions relative to small functions, J. Math. Anal. Appl. 343 (2008), no. 2, 919–931. https://doi.org/10.1016/j.jmaa.2008.02.005
  15. X. M. Li and H. X. Yi, Uniqueness of meromorphic functions whose derivatives share four small functions, J. Math. Anal. Appl. 352 (2009), no. 2, 573–582. https://doi.org/10.1016/j.jmaa.2008.10.007
  16. A. Z. Mokhon’ko, On the Nevanlinna characteristics of some meromorphic functions, in: Theory of Functions, Functional Analysis and Their Applications, vol. 14, Izd-vo Khar’kovsk. Un-ta, 1971, pp. 83–87.
  17. R. Nevanlinna, Einige Eindeutigkeitssatze in der Theorie der Meromorphen Funktionen, Acta Math. 48 (1926), no. 3-4, 367–391. https://doi.org/10.1007/BF02565342
  18. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht, 2003.
  19. H. X. Yi, Meromorphic functions with weighted sharing of three values, Complex Var. Theory Appl. 50 (2005), no. 12, 923–934. https://doi.org/10.1080/02781070500183060
  20. H. X. Yi, On a result of Gross and Yang, Tohoku Math. J. (2) 42 (1990), no. 3, 419–428. https://doi.org/10.2748/tmj/1178227619
  21. H. X. Yi and Y. H. Li, On Osgood-Yang’s conjecture and Mues’ conjecture, Nagoya Math. J. 170 (2003), 163–173. https://doi.org/10.1017/S0027763000008588
  22. Q. C. Zhang, Meromorphic functions sharing three values, Indian J. Pure Appl. Math. 30 (1999), no. 7, 667–682.