Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
권호 표지
DOI QR코드

DOI QR Code

RESULTS ON MEROMORPHIC FUNCTIONS SHARING THREE VALUES WITH THEIR DIFFERENCE OPERATORS

  • LI, XIAO-MIN (DEPARTMENT OF MATHEMATICS OCEAN UNIVERSITY OF CHINA, DEPARTMENT OF PHYSICS AND MATHEMATICS UNIVERSITY OF EASTERN FINLAND) ;
  • YI, HONG-XUN (DEPARTMENT OF MATHEMATICS SHANDONG UNIVERSITY) ;
  • KANG, CONG-YUN (DEPARTMENT OF MATHEMATICS OCEAN UNIVERSITY OF CHINA)
  • Received : 2011.11.10
  • Published : 2015.09.30
Download PDF
⟨ Previous Next ⟩

Abstract

Under the restriction of finite order, we prove two uniqueness theorems of nonconstant meromorphic functions sharing three values with their difference operators, which are counterparts of Theorem 2.1 in [6] for a finite-order meromorphic function and its shift operator.

Keywords

Acknowledgement

Supported by : NSFC

References

  1. A. H. H. Al-khaladi, Meromorphic functions that share three values with one share value for their derivatives, J. Math. (Wuhan) 20 (2000), no. 2, 156-160.
  2. Y. M. Chiang and S. J. Feng, On the Nevanlinna characteristic of $f(z+{\eta})$ and difference equations in the complex plane, Ramanujan J. 16 (2008), no. 1, 105-129. https://doi.org/10.1007/s11139-007-9101-1
  3. R. G. Halburd and R. J. Korhonen, Nevanlinna theory for the difference operator, Ann. Acad. Sci. Fenn. 31 (2006), no. 2, 463-478.
  4. R. G. Halburd and R. J. Korhonen, Difference analogue of the lemma on the logarithmic derivative with applications to difference equations, J. Math. Anal. Appl. 314 (2006), no. 2, 477-487. https://doi.org/10.1016/j.jmaa.2005.04.010
  5. W. K. Hayman, Meromorphic Functions, Clarendon Press, Oxford, 1964.
  6. J. Heittokangas, R. Korhonen, I. Laine, and J. Rieppo, Uniqueness of meromorphic functions sharing values with their shifts, Complex Var. Elliptic Equ. 56 (2011), no. 1-4, 81-92. https://doi.org/10.1080/17476930903394770
  7. J. Heittokangas, R. Korhonen, I. Laine, J. Rieppo, and J. L. Zhang, Value sharing results for shifts of meromorphic functions and sufficient conditions for periodicity, J. Math. Anal. Appl. 355 (2009), no. 1, 352-363. https://doi.org/10.1016/j.jmaa.2009.01.053
  8. I. Lahiri, Weighted sharing of three values and uniqueness of meromorphic functions, Kodai Math. J. 24 (2001), no. 3, 421-435. https://doi.org/10.2996/kmj/1106168813
  9. I. Lahiri and A. Sarkar, On a uniqueness theorem of Tohge, Arch. Math. (Basel) 84 (2005), no. 5, 461-469. https://doi.org/10.1007/s00013-004-1217-6
  10. I. Laine, Nevanlinna Theory and Complex Differential Equations, Walter de Gruyter, Berlin/New York, 1993.
  11. I. Laine and C. C. Yang, Clunie theorems for difference and q-difference polynomials, J. London Math. Soc. 76 (2007), no. 3, 556-566. https://doi.org/10.1112/jlms/jdm073
  12. I. Laine and C. C. Yang, Value distribution of difference polynomials, Proc. Japan Acad. Ser. A Math. Sci. 83 (2007), no. 8, 148-151. https://doi.org/10.3792/pjaa.83.148
  13. X. M. Li and Z. T. Wen, Uniqueness theorems of meromorphis functions sharing three values, Complex Var. Elliptic Equ. 56 (2011), no. 1-4, 215-232. https://doi.org/10.1080/17476933.2010.504834
  14. A. Z. Mokhon'ko, On the Nevanlinna characteristics of some meromorphic functions, In: Theory of Functions, Functional Analysis and Their Applications vol. 14, 83-87, Izd-vo Khar'kovsk, Un-ta, Kharkov, 1971.
  15. J. M. Whittaker, Interpolatory Function Theory, Cambridge Tract No. 33, Cambridge University Press, 1964.
  16. C. C. Yang and H. X. Yi, Uniqueness Theory of Meromorphic Functions, Kluwer Academic Publishers, Dordrecht/Boston/London, 2003.
  17. H. X. Yi, Unicity theorems for meromorphic functions that share three values, Kodai Math. J. 18 (1995), no. 2, 300-314. https://doi.org/10.2996/kmj/1138043427
  18. H. X. Yi, Meromorphic functions with weighted sharing of three values, Complex Var. Theory Appl. 50 (2005), no. 12, 923-934. https://doi.org/10.1080/02781070500183060
  19. J. L. Zhang, Value distribution and shared sets of differences of meromorphic functions, J. Math. Anal. Appl. 367 (2010), no. 2, 401-408. https://doi.org/10.1016/j.jmaa.2010.01.038

Cited by

  1. Meromorphic Functions Sharing Three Values with their Difference Operators vol.17, pp.3, 2017, https://doi.org/10.1007/s40315-016-0188-5
  2. Uniqueness of Meromorphic Functions Sharing Values with Their nth Order Exact Differences pp.1588-273X, 2018, https://doi.org/10.1007/s10476-018-0605-2