|Table of Contents|

[1] Qiu Huiling**,. On Miranda’s Normal Criterion* [J]. Journal of Southeast University (English Edition), 2002, 18 (3): 274-276. [doi:10.3969/j.issn.1003-7985.2002.03.016]
Copy

On Miranda’s Normal Criterion*()
Share：

Journal of Southeast University (English Edition)[ISSN:1003-7985/CN:32-1325/N]

Volumn:
18
Issue:
2002 3
Page:
274-276
Research Field:
Mathematics, Physics, Mechanics
Publishing date:
2002-09-30

Info

Title:
On Miranda’s Normal Criterion*
Author(s):
Qiu Huiling**
Department of Mathematics, Nanjing Normal University, Nanjing 210097, China
Department of Mathematics, Jiangsu Education College, Nanjing 210013, China
Keywords:
entire function;  analytic function;  normality;  differential polynomial
PACS:
O174.52
DOI:
10.3969/j.issn.1003-7985.2002.03.016
Abstract:
In this paper, we study the normality of a family of analytic functions and prove the following theorem. Let F be a family of analytic functions in a domain D, k be a positive integer and a(z), a1(z), a2(z), …, ak(z) be analytic in D such that a(z)≢0. If f(z)≠0 and the zeros of f(k)(z)+a1(z)f(k-1)(z)+…+ak(z)f(z)-a(z) are of multiplicity at least 2 for each f∈F, then Fis normal in D. This result improves Miranda’s normal criterion.

References:

[1] Yang L. Normal families and fix-points of meromorphic functions[J]. Indiana Univ Math J, 1986, 35(1):179-191.
[2] Drasin D. Normal families and the Nevanlinna theory[J]. Acta Math, 1969, 122:231-263.
[3] Zalcman L. A heuristic principle in complex function theory[J]. Amer Math Monthly, 1975, 82:813-817.
[4] Hayman W K. Meromorphic functions[M]. Oxford: Clarendon Press, 1964.
[5] Yang L. Value distribution theory[M]. Berlin:Springer-Verlag & Science Press, 1993.
[6] Schiff J. Normal families[M]. Springer-Verlag, 1993.
[7] Montel P. Leoôle des families normales[J]. L’Enseignement Math, 1934, 33:5-21.
[8] Miranda C. Sur un nouveau critère denormalitè pour les familles de fonctions holomorphes [J]. Bull Soc Math France, 1935, 63:185-196.
[9] Chuang C T. Etude sur les familles normaleset les familles quasi-normales des fonctions mèromorphes[J]. Rendiconti Circolo Math Palermo, 1938, 62:1-80.
[10] Hiong K L, He Y Z. Sur les valeurs multipes des fonctions mèromorphes et de leurs dèrivèes[J]. Sci Sinica, 1961, 10:267-285.
[11] Chen H H, Gu Y X. Improvement of Marty’s criterion and its application[J]. Science in China(series A), 1993, 36:674-681.(in Chinese)

Memo

Memo:
* The project supported by the National Natural Science Foundation of China(10071038)and the National Science Foundation Educational Department of Jiangsu Province(OOKJB110004).
** Born in 1957, female, associate professor.
Last Update: 2002-09-20