Hostname: page-component-586b7cd67f-tf8b9 Total loading time: 0 Render date: 2024-11-20T16:22:19.088Z Has data issue: false hasContentIssue false
  • English
  • Français

Products of spherical derivatives and normal functions

Part of: Entire and meromorphic functions, and related topics

Published online by Cambridge University Press:  09 April 2009

Chen Huaihui  and
Peter Lappan
Chen Huaihui
Affiliation:
Department of Mathematics Nanjing Normal University Nanjing, Jiangsu 210024 Peoples Republic of China e-mail: [email protected]
Peter Lappan
Affiliation:
Department of Mathematics Michigan State UniversityEast Lansing, Michigan 48824USA 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.

Chen and Gu [1] have given some results relating to normal families, and, in this paper, we give versions of these results valid for normal functions. In the process, we improve some of our previous results involving products of certain spherical derivatives as they relate to normal functions. Some examples are given to show the sharpness of our results.

MSC classification

Secondary: 30D05: Functional equations in the complex domain, iteration and composition of analytic functions 30D35: Distribution of values, Nevanlinna theory
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 64 , Issue 2 , April 1998 , pp. 231 - 246
Copyright
Copyright © Australian Mathematical Society 1998

References

[1]Huaihui, Chen and Yong-Xing, Gu, ‘Improvement of Marty's criterion and its application’, Science in China, Ser. A 36 (1993), 674–681.Google Scholar
[2]Huaihui, Chen and Lappan, P., ‘Normal families, orders of zeros, and omitted values’, Ann. Acad. Sci. Fenn. Ser. A I Math. 21 (1996), 89–100.Google Scholar
[3]Lappan, P., ‘The spherical derivative and normal functions’, Ann. Acad. Sci. Fenn. Ser. A I Math. 3 (1977), 301–310.CrossRefGoogle Scholar
[4]Xue-Cheung, Pang, ‘Bloch's principle and normal criterion’, Science in China, Ser. A 32 (1989), 782–791.Google Scholar
[5]Zalcman, L., ‘A heuristic principle in complex function theory’, Amer. Math. Monthly 82 (1975), 813–817.CrossRefGoogle Scholar