Table of Contents Author Guidelines Submit a Manuscript
Abstract and Applied Analysis
Volume 2011, Article ID 239853, 9 pages
http://dx.doi.org/10.1155/2011/239853
Research Article

On Value Distribution of Difference Polynomials of Meromorphic Functions

School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received 24 January 2011; Revised 17 March 2011; Accepted 20 May 2011

Academic Editor: H. B. Thompson

Copyright © 2011 Zong-Xuan Chen. 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, “Picard values of meromorphic functions and their derivatives,” Annals of Mathematics, vol. 70, pp. 9–42, 1959. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  2. Z.-X. Chen and K. H. Shon, “On zeros and fixed points of differences of meromorphic functions,” Journal of Mathematical Analysis and Applications, vol. 344, no. 1, pp. 373–383, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  3. Y.-M. Chiang and S.-J. Feng, “On the Nevanlinna characteristic of f(z+η) and difference equations in the complex plane,” Ramanujan Journal, vol. 16, no. 1, pp. 105–129, 2008. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  4. R. G. Halburd and R. J. Korhonen, “Difference analogue of the lemma on the logarithmic derivative with applications to difference equations,” Journal of Mathematical Analysis and Applications, vol. 314, no. 2, pp. 477–487, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  5. R. G. Halburd and R. J. Korhonen, “Nevanlinna theory for the difference operator,” Annales Academiæ Scientiarium Fennicæ. Mathematica, vol. 31, no. 2, pp. 463–478, 2006. View at Google Scholar · View at Zentralblatt MATH
  6. J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. Zhang, “Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity,” Journal of Mathematical Analysis and Applications, vol. 355, no. 1, pp. 352–363, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  7. K. Liu and I. Laine, “A note on value distribution of difference polynomials,” Bulletin of the Australian Mathematical Society, vol. 81, no. 3, pp. 353–360, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. W. K. Hayman, Meromorphic Functions, Oxford Mathematical Monographs, Clarendon Press, Oxford, UK, 1964.
  9. L. Yang, Value Distribution Theory, Springer, Berlin, Germany, 1993.
  10. A. Z. Mohon'ko, “The Nevanlinna characteristics of certain meromorphic functions,” Teorija Funkciĭ, Funkcional'nyĭ Analiz i ih Priloženija, no. 14, pp. 83–87, 1971. View at Google Scholar
  11. G. Valiron, “Sur la dérivée des fonctions algébroïdes,” Bulletin de la Société Mathématique de France, vol. 59, pp. 17–39, 1931. View at Google Scholar · View at Zentralblatt MATH
  12. F. Gross, Factorization of Meromorhpic Functions, U.S. Government Printing Office, Washinton, DC, USA, 1972.
  13. C.-C. Yang and H.-X. Yi, Uniqueness Theory of Meromorphic Functions, vol. 557 of Mathematics and Its Applications, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003.
  14. J. Wang and I. Laine, “Growth of solutions of nonhomogeneous linear differential equations,” Abstract and Applied Analysis, vol. 2009, Article ID 363927, 11 pages, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH