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Uniqueness of Entire Functions and Differential Polynomials Sharing one Value

  • Zhang, Xiao-Bin (College of Science, Civil Aviation University of China) ;
  • Meng, Da-Wei (College of mathematics and statistics, Xidian University)
  • Received : 2011.03.16
  • Accepted : 2014.01.28
  • Published : 2014.09.23

Abstract

In this paper, we shall utilize Nevanlinna value distribution theory to study the uniqueness problems on entire functions and differential polynomials sharing one value. Our theorems improve or generalize some results of Zhang and Lin, Chen, Zhang, Lin and Chen.

Keywords

References

  1. S. S. Bhoosnurmath, R. S. Dyavanal, Uniqueness and value-sharing of meromorphic functions, Computers and Mathematics with Applications, 53(2007), 1191-1205. https://doi.org/10.1016/j.camwa.2006.08.045
  2. J. F. Chen, X. Y. Zhang, W. C. Lin and S. J. Chen, Uniqueness of entire functions that share one value, Computers and Mathematics with Applications, 56(2008), 3000-3014. https://doi.org/10.1016/j.camwa.2008.07.021
  3. M. L. Fang, Uniqueness and value-sharing of entire functions, Computers and Mathematics with Applications, 44(2002), 828-831
  4. M. L. Fang and X. H. Hua, Entire functions that share one value, Journal of Nanjing University Mathematical Biquarterly, 13(1996), 44-48.
  5. W. K. Hayman, Picard values of meromorphic functions and their derivatives, Annals of Mathematics, 70(1959), 9-42. https://doi.org/10.2307/1969890
  6. L. P. Liu, Uniqueness of meromorphic functions and differential polynomials, Computers and Mathematics with Applications, 56(2008), 3236-3245. https://doi.org/10.1016/j.camwa.2008.09.020
  7. X. G. Qi and J. Dou Some Further Results on Entire Functions That Share Fixed-Points, Kyungpook Math. J., 42(2009), 771-777. https://doi.org/10.5666/KMJ.2009.49.4.771
  8. J. P. Wang, Uniqueness of linear differential polynomials that share the value 1 CM, Kyungpook Math. J., 42(2002), 443-455.
  9. S. M. Wang and Z. S. Gao, Meromorphic Functions Sharing a Small Function, Abstract and Applied Analysis, vol. 2007, Article ID 60718, 6 pages, 2007. doi:10.1155/2007/60718.
  10. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht, The Netherlands, 2003.
  11. C. C. Yang and X. H. Hua, Uniqueness and value-sharing of meromorphic functions, Annales Academioe Scientiarum Fennicoe Mathematica, 22(1997), 395-406.
  12. J. L. Zhang and L. Z. Yang, Some results related to a conjecture of R. Bruck, Journal of Inequalities in Pure and Applied Mathematics, 8(1)(2007), Art. 18.
  13. X. Y. Zhang and W. C. Lin, Uniqueness and value-sharing of entire functions, Journal of Mathematical Analysis and Applications, 343(2008), 938-950. https://doi.org/10.1016/j.jmaa.2008.02.011
  14. X. Y. Zhang and W. C. Lin, Corrigendum to "Uniqueness and value-sharing entire functions" [J. Math. Anal. Appl. 343 (2008 ), 938-950 ], J. Math. Anal. Appl., 352(2009), 971. https://doi.org/10.1016/j.jmaa.2008.10.051
  15. X. B. Zhang and J. F. Xu, Uniqueness of meromorphic functions sharing a small function and its applications, Computers and Mathematics with Applications 61(2011) 722-730.