Skip to main content
SpringerLink
Log in

Normal Families and Shared Values of Meromorphic Functions

  • Published:
Bulletin of the Malaysian Mathematical Sciences Society Aims and scope Submit manuscript

Abstract

Let a and b be two given meromorphic functions on a domain D. We study normality of the family \(\mathcal {F}\) of meromorphic functions that satisfy \(f(z)f ^{(k)}(z) = a(z) \Leftrightarrow f^{(k)}(z) = b(z)\) for every \(f\in \mathcal {F}\) on D. Examples are also given to show the necessity of the conditions in our results.

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

Access this article

Log in via an institution

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

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Hayman, W.K.: Meromorphic Functions. Clarendon, Oxford, UK (1964)

    MATH  Google Scholar 

  2. Schiff, J.L.: Normal Families. Springer, New York (1993)

    Book  MATH  Google Scholar 

  3. Yang, L.: Value Distribution Theory. Spring, Berlin (1993)

    MATH  Google Scholar 

  4. Schwick, W.: Exceptional functions and normality. Bull. Lond. Math. Soc. 29, 425–432 (1997)

    Article  MATH  MathSciNet  Google Scholar 

  5. Liu, D., Deng, B.M., Yang, D.G.: Normal families of meromorphic functions with sharing functions. Bull. Malays. Math. Sci. Soc. (to appear)

  6. Meng, D.W., Hu, P.C.: Normality criteria of meromorphic functions sharing a holomorphic function. Bull. Malays. Math. Sci. Soc. (to appear)

  7. Qi, J.M., Jie, D., Yang, L.Z.: Normality criteria for families of meromorphic function concerning shared values. Bull. Malays. Math. Sci. Soc. 35(2), 449–457 (2012)

    MATH  MathSciNet  Google Scholar 

  8. Xia, J.Y., Xu, Y.: Normality criterion concerning sharing functions II. Bull. Malays. Math. Sci. Soc. 33(3), 479–486 (2010)

    MATH  MathSciNet  Google Scholar 

  9. Zeng, S.P., Lahiri, I.: Montel’s criterion and shared set. Bull. Malays. Math. Sci. Soc. (to appear)

  10. Fang, M.L., Zalcman, L.: Normal families and shared values of meromorphic functions II. Comput. Methods Funct. 1, 289–299 (2001)

    Article  MATH  MathSciNet  Google Scholar 

  11. Chen, H.H., Gu, Y.X.: Improvement of Marty’s criterion and its applications. Sci. China Ser. A 36, 674–681 (1993)

    MATH  MathSciNet  Google Scholar 

  12. Pang, X.C., Zalcman, L.: Normal families and shared values. Bull. Lond. Math. Soc. 32, 325–331 (2000)

    Article  MATH  MathSciNet  Google Scholar 

  13. Wang, Y.F., Fang, M.L.: Picard values and normal families of meromorphic functions with multiple zeros. Acta Mathematica Sinica 14, 17–26 (1998)

    Article  MATH  MathSciNet  Google Scholar 

  14. Bergweiler, W., Pang, X.C.: On the derivative of meromorphic functions with multiple zeros. J. Math. Anal. Appl. 278, 285–292 (2003)

    Article  MATH  MathSciNet  Google Scholar 

Download references

Acknowledgments

This work is supported by the National Natural Science Foundation of China (No. 11171045).

Author information

Authors and Affiliations

  1. Department of Mathematics, Changshu Institute of Technology, Changshu, 215500, Jiangsu, China

    Xiaoyi Liu

Authors
  1. Xiaoyi Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Xiaoyi Liu.

Additional information

Communicated by Saminathan Ponusammy.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Liu, X. Normal Families and Shared Values of Meromorphic Functions. Bull. Malays. Math. Sci. Soc. 39, 155–171 (2016). https://doi.org/10.1007/s40840-015-0166-5

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s40840-015-0166-5

Keywords

Mathematics Subject Classification

Search

Navigation