Arkiv för Matematik

  • Ark. Mat.
  • Volume 38, Number 1 (2000), 171-182.

Normality and shared values

Xuecheng Pang and Lawrence Zalcman

Full-text: Open access

Abstract

LetF be a family of meromorphic functions on the unit disc Δ and let a and b be distinct values. If for every fF, f and f′ share a and b on Δ, then F is normal on Δ.

Note

The first author was supported by NNSF of China approved no. 19771038 and by the Research Institute for Mathematical Sciences, Bar-Ilan University.

Article information

Source
Ark. Mat., Volume 38, Number 1 (2000), 171-182.

Dates
Received: 10 August 1998
First available in Project Euclid: 31 January 2017

Permanent link to this document
https://projecteuclid.org/euclid.afm/1485898672

Digital Object Identifier
doi:10.1007/BF02384496

Mathematical Reviews number (MathSciNet)
MR1749364

Zentralblatt MATH identifier
1079.30044

Rights
2000 © Institut Mittag-Leffler

Citation

Pang, Xuecheng; Zalcman, Lawrence. Normality and shared values. Ark. Mat. 38 (2000), no. 1, 171--182. doi:10.1007/BF02384496. https://projecteuclid.org/euclid.afm/1485898672


Export citation

References

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