Arkiv för Matematik

, Volume 38, Issue 1, pp 171–182 | Cite as

Normality and shared values

  • Xuecheng Pang
  • Lawrence Zalcman
Article

Abstract

LetF be a family of meromorphic functions on the unit disc Δ and leta andb be distinct values. If for everyfF,f andf′ sharea andb on Δ, thenF is normal on Δ.

Keywords

Unit Disc Meromorphic Function 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Bergweiler, W. andEremenko, A., On the singularities of the inverse to a meromorphic function of finite order,Rev. Mat. Iberoamericana 11 (1995), 355–373.MathSciNetGoogle Scholar
  2. 2.
    Chen, H. andGu, Y., An improvement of Marty's criterion and its applications,Sci. China Ser. A 36 (1993), 674–681.MathSciNetGoogle Scholar
  3. 3.
    Clunie, J. andHayman, W. K., The spherical derivative of integral and meromorphic functions,Comment. Math. Helv. 40, (1966), 117–148.MathSciNetGoogle Scholar
  4. 4.
    Frank, G. andWeissenborn, G., Rational deficient functions of meromorphic functions,Bull. London Math. Soc. 18 (1986), 29–33.MathSciNetGoogle Scholar
  5. 5.
    Hayman, W. K., Picard values of meromorphic functions and their derivatives,Ann. of Math. 70 (1959), 9–42.MATHMathSciNetGoogle Scholar
  6. 6.
    Hayman, W. K.,Meromorphic Functions, Clarendon Press, Oxford, 1964.Google Scholar
  7. 7.
    Minda, D., Yosida functions, inLectures on Complex Analysis (Chuang, C.-T., ed.), pp. 197–213, World Scientific Publ., Singapore, 1988.Google Scholar
  8. 8.
    Mues, E. andSteinmetz, N., Meromorphe Funktionen, die mit ihrer Ableitung Werte teilen,Manuscripta Math. 29 (1979), 195–206.CrossRefMathSciNetGoogle Scholar
  9. 9.
    Pang, X., On normal criterion of meromorphic functions,Sci. China Ser. A 33 (1990), 521–527.MATHMathSciNetGoogle Scholar
  10. 10.
    Pang, X., Shared values and normal families, Preprint, 1998.Google Scholar
  11. 11.
    Pang, X. andZalcman, L., Normal families and shared values, to appear inBull. London Math. Soc. Google Scholar
  12. 12.
    Schwick, W., Sharing values and normality,Arch. Math. (Basel) 59 (1992), 50–54.MATHMathSciNetGoogle Scholar
  13. 13.
    Yang, L.,Value Distribution Theory, Springer-Verlag, Berlin-Heidelberg, 1993.Google Scholar

Copyright information

© Institut Mittag-Leffler 2000

Authors and Affiliations

  • Xuecheng Pang
    • 1
  • Lawrence Zalcman
    • 2
  1. 1.Department of MathematicsEast China Normal UniversityShanghaiP. R. China
  2. 2.Department of Mathematics and Computer ScienceBar-Ilan UniversityRamat-GanIsrael

Personalised recommendations