About this Journal Submit a Manuscript Table of Contents
Abstract and Applied Analysis
Volume 2013 (2013), Article ID 273040, 6 pages
http://dx.doi.org/10.1155/2013/273040
Research Article

Results on Difference Analogues of Valiron-Mohon'ko Theorem

1Department of Mathematics, Guangdong University of Education, Guangzhou 510303, China
2School of Mathematical Sciences, South China Normal University, Guangzhou 510631, China

Received 6 April 2013; Accepted 4 May 2013

Academic Editor: Allan Peterson

Copyright © 2013 Ran Ran Zhang and Zhi Bo Huang. 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. View at MathSciNet
  2. L. Yang, Value Distribution Theory and New Research, Science Press, Beijing, China, 1982.
  3. I. Laine, Nevanlinna theory and complex differential equations, Walter de Gruyter, Berlin, Germany, 1993. View at Publisher · View at Google Scholar · View at MathSciNet
  4. W. Bergweiler and J. K. Langley, “Zeros of differences of meromorphic functions,” Mathematical Proceedings of the Cambridge Philosophical Society, vol. 142, no. 1, pp. 133–147, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  5. Z. X. Chen, Z. B. Huang, and X. M. Zheng, “On properties of difference polynomials,” Acta Mathematica Scientia B, vol. 31, no. 2, pp. 627–633, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  6. Z. X. Chen and K. H. Shon, “Estimates for the zeros of differences of meromorphic functions,” Science in China A, vol. 52, no. 11, pp. 2447–2458, 2009. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  7. 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 · View at MathSciNet
  8. 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 · View at MathSciNet
  9. I. Laine and C.-C. Yang, “Clunie theorems for difference and q-difference polynomials,” Journal of the London Mathematical Society, vol. 76, no. 3, pp. 556–566, 2007. View at Publisher · View at Google Scholar · View at MathSciNet
  10. I. Laine and C.-C. Yang, “Value distribution of difference polynomials,” Japan Academy A, vol. 83, no. 8, pp. 148–151, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  11. R. R. Zhang and Z. X. Chen, “Value distribution of difference polynomials of meromorphic functions,” Science China Mathematics, vol. 42, no. 11, pp. 1115–1130, 2012.
  12. R. R. Zhang and Z. X. Chen, “Value distribution of meromorphic functions and their differences,” Turkish Journal of Mathematics, vol. 36, no. 3, pp. 395–406, 2012. View at MathSciNet
  13. R. Korhonen and O. Ronkainen, “Order reduction method for linear difference equations,” Proceedings of the American Mathematical Society, vol. 139, no. 9, pp. 3219–3229, 2011. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  14. C.-C. Yang and I. Laine, “On analogies between nonlinear difference and differential equations,” Japan Academy A, vol. 86, no. 1, pp. 10–14, 2010. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  15. R. G. Halburd and R. J. Korhonen, “Meromorphic solutions of difference equations, integrability and the discrete Painlevé equations,” Journal of Physics A, vol. 40, no. 6, pp. R1–R38, 2007. View at Publisher · View at Google Scholar · View at Zentralblatt MATH · View at MathSciNet
  16. A. A. Gol'dberg and I. V. Ostrovskii, Distribution of Values of Meromorphic Functions, Nauka, Moscow, Russia, 1970.