Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-10T15:42:06.486Z Has data issue: false hasContentIssue false
  • English
  • Français

On normal families of meromorphic functions

Published online by Cambridge University Press:  09 April 2009

Yan Xu  and
Mingliang Fang
Mingliang Fang
Affiliation:
Department of Mathematics Nanjing Normal UniversityNanjing 210097 P. R.China e-mail: yanxu@email.njnu.edu.cn, mlfang@pine.njnu.edu.cn
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

In this paper we obtain some normality criteria of families of meromorphic functions, which improve and generalize the related results of Gu and Bergweiler, respectively. Some examples are given to show the sharpness of our results.

Keywords

meromorphic functionnormal familyresidue.
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 74 , Issue 2 , April 2003 , pp. 155 - 164
Copyright
Copyright © Australian Mathematical Society 2003

References

[1]Bergweiler, W., ‘On the zeros of certyain homogeneous differential polynomials’, Arch. Math. 64 (1995), 199–202.CrossRefGoogle Scholar
[2]Bergweiler, W., ‘Normality and exceptional values of derivates’, Proc. Amer. Math. Soc. 129 (2000), 121–129.CrossRefGoogle Scholar
[3]Bergweiler, W. and Eremenko, A., ‘On the singularities of the inverse to a meromorphic function of finite order’, Rev. Mat. Iberoam 11 (1995), 355–373.CrossRefGoogle Scholar
[4]Chen, H. H. and Gu, Y. X., ‘An improvement of Marty's criterion and its applications’, Sci. China, Ser. A 36 (1993), 674–681.Google Scholar
[5]Gu, Y. X., ‘A normal criterion of meromorphic families’, Scientia Sinica, Math. Issue 1 (1979), 267–274.Google Scholar
[6]Hayman, W. K., ‘Picard values of meromorphic functions and their derivatives’, Ann. of Math. (2) 70 (1959), 9–42.CrossRefGoogle Scholar
[7]Hayman, W. K., Meromorphic functions (Clarendon Press, Oxford, 1964).Google Scholar
[8]Hayman, W. K., Research problems in function theory (Athlone Press, London, 1967).Google Scholar
[9]Peng, X. C. and Zalcman, L., ‘Normal families and shared values’, Bull. London Math. Soc. 18 (1995), 437–450.Google Scholar
[10]Rippon, P. J. and Stallard, G. M., ‘Iteration of a class of hyperbolic meromorphic functions’, Proc. Amer. Math. Soc. (to appear).Google Scholar
[11]Wang, Y. F. and Fang, M. L., ‘Picard values and normal families of meromorphic functions with multiple zeros’, Acta Math. Sin., New Ser. 14 (1) (1998), 17–26.Google Scholar