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Abstract and Applied Analysis
Volume 2012, Article ID 896596, 13 pages
http://dx.doi.org/10.1155/2012/896596
Research Article

The Uniqueness of Analytic Functions on Annuli Sharing Some Values

1Department of Informatics and Engineering, Jingdezhen Ceramic Institute, Jingdezhen 333403, China
2Beijing Key Laboratory of Information Service Engineering, Department of General Education, Beijing Union University, No. 97 Bei Si Huan Dong Road, Chaoyang District, Beijing 100101, China

Received 28 March 2012; Accepted 11 July 2012

Academic Editor: Patricia J. Y. Wong

Copyright © 2012 Hong-Yan Xu and Zu-Xing Xuan. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, UK, 1964.
  2. H.-X. Yi and C.-C. Yang, Uniqueness Theory of Meromorphic Functions, Science Press 1995, Kluwer, 2003.
  3. L. Yang, Value Distribution Theory, Springer, Berlin, Germany, 1993.
  4. R. Nevanlinna, “Eindentig keitssätze in der theorie der meromorphen funktionen,” Acta Mathematica, vol. 48, no. 3-4, pp. 367–391, 1926. View at Publisher · View at Google Scholar
  5. J.-H. Zheng, “On uniqueness of meromorphic functions with shared values in one angular domain,” Complex Variables, vol. 48, no. 9, pp. 777–785, 2003. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  6. A. Banerjee, “Weighted sharing of a small function by a meromorphic function and its derivative,” Computers & Mathematics with Applications, vol. 53, no. 11, pp. 1750–1761, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. S. S. Bhoosnurmath and R. S. Dyavanal, “Uniqueness and value-sharing of meromorphic functions,” Computers & Mathematics with Applications, vol. 53, no. 8, pp. 1191–1205, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. T.-B. Cao and H.-X. Yi, “On the uniqueness of meromorphic functions that share four values in one angular domain,” Journal of Mathematical Analysis and Applications, vol. 358, no. 1, pp. 81–97, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. W. Lin, S. Mori, and K. Tohge, “Uniqueness theorems in an angular domain,” The Tohoku Mathematical Journal, vol. 58, no. 4, pp. 509–527, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  10. H.-Y. Xu, C.-F. Yi, and T.-B. Cao, “Uniqueness of meromorphic functions and differential polynomials sharing one value with finite weight,” Annales Polonici Mathematici, vol. 95, no. 1, pp. 51–66, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  11. X.-Y. Zhang, J.-F. Chen, and W.-C. Lin, “Entire or meromorphic functions sharing one value,” Computers & Mathematics with Applications, vol. 56, no. 7, pp. 1876–1883, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. J.-H. Zheng, “On uniqueness of meromorphic functions with shared values in some angular domains,” Canadian Mathematical Bulletin, vol. 47, no. 1, pp. 152–160, 2004. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  13. S. Axler, “Harmonic functions from a complex analysis viewpoint,” The American Mathematical Monthly, vol. 93, no. 4, pp. 246–258, 1986. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  14. A. Ya. Khrystiyanyn and A. A. Kondratyuk, “On the Nevanlinna theory for meromorphic functions on annuli. I,” Matematychni Studii, vol. 23, no. 1, pp. 19–30, 2005. View at Google Scholar · View at Zentralblatt MATH
  15. A. Ya. Khrystiyanyn and A. A. Kondratyuk, “On the Nevanlinna theory for meromorphic functions on annuli. II,” Matematychni Studii, vol. 24, no. 2, pp. 57–68, 2005. View at Google Scholar · View at Zentralblatt MATH
  16. A. A. Kondratyuk and I. Laine, “Meromorphic functions in multiply connected domains,” in Fourier Series Methods in Complex Analysis, I. Laine, Ed., vol. 10 of Proceedings of the workshop, Mekrijärvi, Finland, July 24-29, 2005, pp. 9–111, Report series, Department of Mathematics University of Joensuu, Joensuu, Finland, 2006. View at Google Scholar
  17. T. B. Cao and H. X. Yi, “Uniqueness theorems for meromorphic functions sharing sets IM on annuli,” Acta Mathematica Sinica, vol. 54, no. 4, pp. 623–632, 2011 (Chinese). View at Google Scholar
  18. T.-B. Cao, H.-X. Yi, and H.-Y. Xu, “On the multiple values and uniqueness of meromorphic functions on annuli,” Computers & Mathematics with Applications, vol. 58, no. 7, pp. 1457–1465, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH