Skip to main content
Log in

On the Uniqueness Theory of Entire Functions and Their Difference Operators

  • Published:
Complex Analysis and Operator Theory Aims and scope Submit manuscript

Abstract

In this paper, we consider uniqueness problems on entire functions that share a small periodic entire functions with their shifts and difference operators, we improve also some results due to B. Chen, Z. X. Chen and S. Li.

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

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. Bergweiler, W., Langley, J.K.: Zeros of differences of meromorphic functions. Math. Proc. Camb. Philos. Soc. 142(1), 133-147 (2007)

    Article  MathSciNet  MATH  Google Scholar 

  2. Chen, B., Chen, Z.X., Li, S.: Uniqueness problems on entire functions and their difference operators or shifts. Abstr. Appl. Anal. 2012. Article ID 906893 (2012)

  3. Chen, B., Li, S.: Uniqueness theorems on entire functions that share small functions with their difference operators. Adv. Diff. Equ. 2014, 311 (2014)

    Article  Google Scholar 

  4. Chen, Z.X.: Complex differences and difference equations, mathematics monograph series 29. Science Press, Beijing (2014)

    Google Scholar 

  5. Chiang, Y.M., Feng, S.J.: On the Nevanlinna characteristic of $f\left( z+\eta \right)$ and difference equations in the complex plane. Ramanujan J. 16(1), 105-129 (2008)

    Article  MathSciNet  MATH  Google Scholar 

  6. Halburd, R.G., Korhonen, R.J.: Difference analogue of the lemma on the logarithmic derivative with applications to difference equations. J. Math. Anal. Appl. 314(2), 477-487 (2006)

    Article  MathSciNet  MATH  Google Scholar 

  7. Halburd, R.G., Korhonen, R.J.: Nevanlinna theory for the difference operator. Ann. Acad. Sci. Fenn. Math. 31(2), 463-478 (2006)

    MathSciNet  MATH  Google Scholar 

  8. Hayman, W.K.: Meromorphic functions. Oxford Mathematical Monographs Clarendon Press, Oxford (1964)

    MATH  Google Scholar 

  9. Heittokangas, J., Korhonen, R., Laine, I., Rieppo, J., Zhang, J.: Value sharing results for shifts of meromorphic functions, and sufficient conditions for periodicity. J. Math. Anal. Appl. 355, 352-363 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  10. Jank, G., Mues, E., Volkmann, L.: Meromorphe funktionen, die mit ihrer ersten und zweiten ableitung einen endlichen wert teilen. Complex Var. Theory Appl. 6(1), 51-71 (1986)

    Article  MathSciNet  MATH  Google Scholar 

  11. Laine, I.: Nevanlinna theory and complex differential equations, de Gruyter studies in mathematics, 15. Walter de Gruyter & Co., Berlin (1993)

    Book  Google Scholar 

  12. Rubel, L.A., Yang, C.C.: Values shared by an entire function and its derivatives, lecture notes in math, vol. 599, pp. 101-103. Springer, Berlin (1977)

    Google Scholar 

  13. Qi, X.G., Yang, L.Z., Liu, K.: Uniqueness and periodicity of meromorphic functions concerning the difference operator. Comput. Math. Appl. 60, 1739-1746 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  14. Yang, C.C., Yi, H.X.: Uniqueness theory of meromorphic functions, Mathematics and its Applications, 557. Kluwer Academic Publishers Group, Dordrecht (2003)

    Book  Google Scholar 

Download references

Acknowledgments

The authors would like to thank the anonymous referee for his/her helpful remarks and suggestions to improve this article.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Zinelâabidine Latreuch.

Additional information

Communicated by Ronen Peretz.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

El Farissi, A., Latreuch, Z. & Asiri, A. On the Uniqueness Theory of Entire Functions and Their Difference Operators. Complex Anal. Oper. Theory 10, 1317–1327 (2016). https://doi.org/10.1007/s11785-015-0514-3

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11785-015-0514-3

Keywords

Mathematics Subject Classification

Navigation