Value distribution of general differential-difference polynomials of meromorphic functions


In this paper, by reducing the conditions on the zeros and poles of a finite order meromorphic function f(z), we improve the results by Zheng and Chen (Acta. Math. Sin. 54, 983–992 [12]) and Zheng and Xu (Abstr. Appl. Anal. 12 pages [13]).

This is a preview of subscription content, log in to check access.


  1. 1.

    Chen, Z. X. (2011). On value distribution of difference polynomials of meromorphic functions, Abstr. Appl. Anal., 2011 (Article ID 239853).

  2. 2.

    Chiang, Y.M., and S.J. Feng. 2008. On the Nevanlinna characteristic of \(f(z+\eta )\) and difference equations in the complex plane. Ramanujan J. 16: 105–129.

    Google Scholar 

  3. 3.

    Halburd, R.G., and R.J. Korhonen. 2006. Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J. Math. Anal. Appl. 314: 477–487.

    MathSciNet  Article  Google Scholar 

  4. 4.

    Hayman, W.K. 1964. Meromorphic functions. Oxford: Clarendon Press.

    Google Scholar 

  5. 5.

    Laine, I. 1993. Nevanlinna theory and complex differential equations. Berlin: de Gruyter.

    Google Scholar 

  6. 6.

    Lan, S., and Z. Chen. 2013. Zeros of some difference polynomials. Adv. Diff. Equ. 2013: 194.

    MathSciNet  Article  Google Scholar 

  7. 7.

    Laine, I., and C.C. Yang. 2007. Clunie theorems for difference and \(q\)-difference polynomials. J. Lond. Math. Soc. 2 (76): 556–566.

    Google Scholar 

  8. 8.

    Yang, C.C., and I. Laine. 2010. On analogies between nonlinear difference and differential equations. Proc. Jpn. Acad. Ser. A. Math. Sci. 86 (1): 10–14.

    MathSciNet  Article  Google Scholar 

  9. 9.

    Yang, C.C., and H.X. Yi. 2003. Uniqueness theory of meromorphic functions. Dordrecht: Kluwer Academic Publishers.

    Google Scholar 

  10. 10.

    Yang, L. 1982. Value distribution theory and its new research. Beijing: Science Press. (In Chinese).

    Google Scholar 

  11. 11.

    Zheng, X.M., and Z.X. Chen. 2013. On the value distribution of some difference polynomials. J. Math. Anal. Appl. 397: 814–821.

    MathSciNet  Article  Google Scholar 

  12. 12.

    Zheng, X.M., and Z.X. Chen. 2011. On deficiencies of some difference polynomials. Acta. Math. Sin. 54: 983–992. (In Chinese).

    MathSciNet  MATH  Google Scholar 

  13. 13.

    Zheng, X.M., H.Y. Xu. 2014. On the deficiencies of some differential-difference polynomials. Abstr. Appl. Anal, pp 12

Download references


The authors are thankful to the referees for their valuable suggestions towards the improvement of the paper. First author is supported by UGC-SAP DRS-III, Department of Mathematics, Karnatak University, Dharwad. Ref. No. F.510/3/DRS-III/2016(SAP-I) Dated: 29th February 2016 and the second author was supported by UGC-UPE fellowship, Department of Mathematics, Karnatak University, Dharwad. Ref. No. KU/Sch/UGC-UPE/2014-15/894.

Author information



Corresponding author

Correspondence to Renukadevi S. Dyavanal.

Additional information

Publisher's note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Dyavanal, R.S., Mathai, M.M. Value distribution of general differential-difference polynomials of meromorphic functions. J Anal 27, 931–942 (2019).

Download citation


  • Meromorphic function f(z)
  • Deficiency of zeros and poles of f(z)
  • Order of f(z) and differential-difference polynomials of  f(z)

Mathematics Subject Classification

  • 30D35
  • 39A05