Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-23T17:49:28.841Z Has data issue: false hasContentIssue false
  • English
  • Français

On Rosenbloom's fixed-point theorem and related results

Published online by Cambridge University Press:  09 April 2009

Mingliang Fang  and
Wenjun Yuan
Mingliang Fang
Affiliation:
State Key Laboratory of millimetre waves Southeast UniversityNanjing 210096 or Department of Mathematics Nanjing Normal UniversityNanjing 210097 P.R.China e-mail: [email protected]
Wenjun Yuan
Affiliation:
Department of Mathematics Guan Zhou Normal UniversityGuan Zhou, 510405 P.R.China e-mail: [email protected]
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 improve the Rosenbloom's fixed-point theorem and prove a related normality criterion. We also consider the corresponding unicity theorem for transcendental entire functions.

Keywords

Entire functionfixed-pointnormal criterionunicity theorem
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 68 , Issue 3 , June 2000 , pp. 321 - 333
Copyright
Copyright © Australian Mathematical Society 2000

References

[1]Chuang, C. T. and Yang, C. C., Fixed points and factorization theory for meromorphic functions (World Scientific, Singapore, 1990).Google Scholar
[2]Gross, F., Factorization of meromorphic functions and some open problems, Lecture Notes in Math. 599 (Springer, 1977).CrossRefGoogle Scholar
[3]Gu, Y. X., ‘A normal criterion of meromorphic families’, Scientia Sinica 1 (1979), 267–274.Google Scholar
[4]Gundersen, G. G., ‘Meromorphic functions that share four values’, Trans. Amer. Math. Soc. 277 (1983), 545–567; ‘Correction to ‘Meromorphic functions that share four values’, Trans. Amer. Math. Soc., 304 (1987), pp. 847–850.CrossRefGoogle Scholar
[5]Hayman, W. K., Meromorphic functions (Clarendon Press, Oxford, 1964).Google Scholar
[6]Rosenbloom, P. C., ‘The fix-points of entire functions’, Comm. Sém. Math. Univ. Lund [Medd. Lunds Univ. Mat. Sem.] 1952 (1952), Tom Supplementaire, 186–192.Google Scholar
[7]Schiff, J., Normal families (Springer, Berlin, 1993).CrossRefGoogle Scholar
[8]Yang, L., ‘Normal families and fix-points of meromorphic functions’, Indiana Univ. Math. J. 35 (1986), 179–191.CrossRefGoogle Scholar
[9]Yi, H. X., ‘A question of Gross and uniqueness of meromorphic functions’, Nagoya Math. J. 33 (1995), 521–527.Google Scholar
[10]Yi, H. X. and Yang, C. C., Unicity theory of meromorphic functions (Science Press, Beijing, 1995).Google Scholar
[11]Zalcman, L., ‘A heuristic principle in complex function theory’, Amer. Math. Monthly 82 (1975), 813–817.CrossRefGoogle Scholar
[12]Zheng, J. H. and Yang, C. C., ‘Further results on fixpoints and zeros of entrire functions’, Trans. Amer. Math. Soc. 347 (1995), 37–50.CrossRefGoogle Scholar