DOI QR코드

DOI QR Code

Uniqueness of Meromorphic Functions Concerning the Difference Polynomials

  • LIU, FANGHONG (Department of Foundation, Shandong Xiehe University, School of mathimatics, Shandong University) ;
  • YI, HONGXUN (Department of Foundation, Shandong Xiehe University, School of mathimatics, Shandong University)
  • 투고 : 2014.05.13
  • 심사 : 2014.09.19
  • 발행 : 2015.06.23

초록

In this article, we main study the uniqueness problem of meromorphic function which difference polynomials sharing common values. We consider the entire function $(f^n(f^m-1)\prod_{j=1}^{s}f(z+c_j)^{{\mu}j})^{(k)}$ and the meromorphic function $f^n(f^m-1)\prod_{j=1}^{s}f(z+c_j)^{{\mu}j}$ to get the main results which extend Theorem 1.1 in paper[5] and theorem 1.4 in paper[6].

키워드

과제정보

연구 과제 주관 기관 : National Natural Science Foundation of China

참고문헌

  1. C. C. Yangand H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht, 2003.
  2. X. G. Qi, L. Z. Yang and K. Liu, Uniqueness and periodicity of meromorphic functions concerning the difference operator, Computer and Mathematics with Applications., 60(2010), 1739-1746. https://doi.org/10.1016/j.camwa.2010.07.004
  3. C, Y. Fang. and M, L. Fang., Uniqueness of meromorphic functions and differential polynomials, Comput. Math. Appl., 44(2002), 607-617. https://doi.org/10.1016/S0898-1221(02)00175-X
  4. SS Bhoosnurmathand SR Kabbur, Value Distribution and Uniqueness Theorems for Difference of Entire and Meromorphic Functions, International Journal of Analysis and Applications, 2013, 124-136.
  5. Keyu Zhang, Hongxun Yi, the Value Distribution and Uniqueness of one Certain Type of Differental-Difference Polynomials, Acta Mathematica Scientis Series Manuscript, 34B(3)(2014), 719-728.
  6. Li, Yi and Li, Value distribution of certain difference polynomials of meromorphic functions, Rocky Mountain J. Math. Volume forthcoming, Number forthcoming (2013).
  7. Monhon'ko A, The Nevalinna characteristics of certain meromorphic function [J], Teor Funksii Funktsional Anal I Prilozhen, 1971, 14:83-87 (in Russian).
  8. JL Zhang and LZ Yang, Some results related to a conjecture of R, Brck. J. Inequal. Pure Appl. Math., 2007.
  9. Chen M R and Chen Z X, Properties of Difference Polynomials of Entire Functions with Finite Order, Chinese Annals of Mathematics, 33A(3)(2012), 359-374 (in chinese).
  10. R. G. Halburd and R. Korhonen., Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl., 314(2006), 477C487. https://doi.org/10.1016/j.jmaa.2005.04.010
  11. Xiao Min Li and Hong Xun Yi, Entire Functions Sharing an Entire Function of Smaller Order with Their Difference Operators, Acta Mathematica Sinica, English Series Mar., 30(3)(2014), 481C498. https://doi.org/10.1007/s10114-014-2042-x
  12. Zhang R R and Chen Z X, Value distribution Difference Polynomials of meromorphic functions, Chinese Science, Mathematics: Mathematics, 42(11)(2012), 1115-1130(in chinese).
  13. Xiao-Min Li, Hong-Xun Yi and Yue Shi, Value Sharing of Certain Differential Polynomials and Their Shifts of Meromorphic Functions, Comput. Methods Funct. Theory DOI 10.1007/s40315-014-0048-0 2014.
  14. Xudan Luo and Weichuan Lin., Value sharing results for shifts of meromorphic functions, J. Math. Anal.Appl. 377(2011),441C449. https://doi.org/10.1016/j.jmaa.2010.10.055
  15. Raj Shree Dhar., Uniqueness Theorems on Meromorphic Functions and their Difference Operators, Int. Journal of Math. Analysis, 7(3)(2013), 1489-1495.
  16. Baoqin Chen, Zongxuan Chen and Sheng Li, Uniqueness of difference operators of meromorphic functions, Journal of Inequalities and Applications 2012, 2012:48. https://doi.org/10.1186/1029-242X-2012-48
  17. HongYan Xu, On the value distribution and uniqueness of difference polynomials of meromorphic functions, Advances in Difference Equations 2013, 2013:90. https://doi.org/10.1186/1687-1847-2013-90
  18. Sheng Li and BaoQin Chen, Meromorphic functions sharing small functions with their linear difference polynomials, Advances in Difference Equations 2013, 2013:58. https://doi.org/10.1186/1687-1847-2013-58

피인용 문헌

  1. On the uniqueness of certain types of differential-difference polynomials vol.43, pp.3, 2017, https://doi.org/10.1007/s10476-017-0402-3