Hostname: page-component-7dd5485656-zklqj Total loading time: 0 Render date: 2025-10-31T03:51:20.007Z Has data issue: false hasContentIssue false
  • English
  • Français

Normality and exceptional functions of derivatives

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Yan Xu
Yan Xu
Affiliation:
Department of Mathematics, Nanjing Normal University, Nanjing 210097, P. R. China e-mail: xuyan@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 for families of meromorphic functions that concern the exceptional functions of derivatives, which improve and generalize related results of Gu, Yang, Schwick, Wang-Fang, and Pang-Zalcman. Some examples are given to show the sharpness of our results.

Keywords

meromorphic functionnormal familyexceptional functions

MSC classification

Secondary: 30D35: Distribution of values, Nevanlinna theory

Information

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 76 , Issue 3 , June 2004 , pp. 403 - 414
Copyright
Copyright © Australian Mathematical Society 2004

References

[1]Berweiler, W., ‘Normality and exceptional values of derivatives’, Proc. Amer. Math. Soc. 129 (2000), 121–129.CrossRefGoogle Scholar
[2]Chen, H. H., ‘Yosida function and Picard values of integral functions and their derivatives’, Bull. Austral. Math. Soc. 54 (1996), 373–381.Google Scholar
[3]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
[4]Fang, M. L., ‘A note on a problem of Hayman’, Analysis 20 (2000), 45–49.CrossRefGoogle Scholar
[5]Fang, M. L., ‘Picard values and normality criterion’, Bull. Korean Math. Soc. 38 (2001), 379–387.Google Scholar
[6]Gu, Y. X., ‘A normal criterion of meromorphic families’, Scientia Sinica, Math. Issue 1 (1979), 267–274.Google Scholar
[7]Hayman, W. K., ‘Picard values of meromorphic functions and their derivatives’, Ann. of Math. (2) 70 (1959), 9–42.CrossRefGoogle Scholar
[8]Hayman, W. K., Meromorphic functions (Clarendon Press, Oxford, 1964).Google Scholar
[9]Hayman, W. K., Research problems in function theory (Athlone Press, London, 1967).Google Scholar
[10]Pang, X. C. and Zalcman, L., ‘Normal families of meromorphic functions with multiple zeros and poles’, Israel J. Math. 136 (2003), 1–9.CrossRefGoogle Scholar
[11]Pang, X. C. and Zalcman, L., ‘Normal families and shared values’, Bull. London Math. Soc. 18 (1995), 437–450.Google Scholar
[12]Schiff, J., Normal families (Springer, New York, 1993).CrossRefGoogle Scholar
[13]Schwick, W., ‘Exceptional functions and normality’, Bull. London Math. Soc. 29 (1997), 425–432.CrossRefGoogle Scholar
[14]Schwick, W., ‘On Hayman's alternative for families of meromorphic functions’, Complex Variables Theory Appl. 32 (1997), 51–57.Google Scholar
[15]Wang, Y. F., ‘On Mues conjecture and Picard values’, Sci. China 36 (1993), 28–35.Google Scholar
[16]Wang, Y. F. and Fang, M. L., ‘Picard values and normal families of meromorphic functions with multiple zeros’, Acta. Math. Sinica (N.S.) 14 (1998), 17–26.Google Scholar
[17]Xu, Y. and Fang, M. L., ‘On normal families of meromorphic functions’, J. Aust. Math. Soc. 74 (2003), 155–164.CrossRefGoogle Scholar
[18]Yang, L., ‘Normal families and fixed-points of meromorphic functions’, Indiana Univ. Math. J. 35 (1986), 179–191.CrossRefGoogle Scholar
[19]Yang, L., ‘Normality of families of meromorphic functions’, Sci. China 9 (1986), 898–908.Google Scholar
[20]Yang, L., Value distribution theory (Springer, Berlin; Science Press, Beijing, 1993).Google Scholar
[21]Zalcman, L., ‘A heuristic principle in complex function theory’, Amer. Math. Monthly 82 (1975), 813–817.CrossRefGoogle Scholar
[22]Zalcman, L., Normal families: new perspectives', Bull. Amer. Math. Soc. 35 (1998), 215–230.CrossRefGoogle Scholar