Advertisement

Value distribution of general differential-difference polynomials of meromorphic functions

  • Renukadevi S. DyavanalEmail author
  • Madhura M. Mathai
Original Research Paper
  • 5 Downloads

Abstract

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]).

Keywords

Meromorphic function f(zDeficiency of zeros and poles of f(zOrder of f(z) and differential-difference polynomials of  f(z) 

Mathematics Subject Classification

30D35 39A05 

Notes

Acknowledgements

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.

References

  1. 1.
    Chen, Z. X. (2011). On value distribution of difference polynomials of meromorphic functions, Abstr. Appl. Anal., 2011 (Article ID 239853).Google Scholar
  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.MathSciNetCrossRefGoogle 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.MathSciNetCrossRefGoogle Scholar
  4. 4.
    Hayman, W.K. 1964. Meromorphic functions. Oxford: Clarendon Press.zbMATHGoogle Scholar
  5. 5.
    Laine, I. 1993. Nevanlinna theory and complex differential equations. Berlin: de Gruyter.CrossRefGoogle Scholar
  6. 6.
    Lan, S., and Z. Chen. 2013. Zeros of some difference polynomials. Adv. Diff. Equ. 2013: 194.MathSciNetCrossRefGoogle 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.MathSciNetCrossRefGoogle 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.MathSciNetCrossRefGoogle Scholar
  9. 9.
    Yang, C.C., and H.X. Yi. 2003. Uniqueness theory of meromorphic functions. Dordrecht: Kluwer Academic Publishers.CrossRefGoogle 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.MathSciNetCrossRefGoogle 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).MathSciNetzbMATHGoogle Scholar
  13. 13.
    Zheng, X.M., H.Y. Xu. 2014. On the deficiencies of some differential-difference polynomials. Abstr. Appl. Anal, pp 12Google Scholar

Copyright information

© Forum D'Analystes, Chennai 2018

Authors and Affiliations

  1. 1.Department of MathematicsKarnatak UniversityDharwadIndia

Personalised recommendations