Annales Academić Scientiarum Fennicć
Mathematica
Volumen 38, 2013, 691-695

A GENERAL DIFFERENTIAL INEQUALITY OF THE kTH DERIVATIVE THAT LEADS TO NORMALITY

Qiaoyu Chen, Shahar Nevo and Xuecheng Pang

East China Normal University, Department of Mathematics
Shanghai 200241, P.R. China; goodluckqiaoyu 'at' 126.com

Bar-Ilan University, Department of Mathematics
Ramat-Gan 52900, Israel; nevosh 'at' macs.biu.ac.il

East China Normal University, Department of Mathematics
Shanghai 200241, P.R. China; xcpang 'at' math.ecnu.edu.cn

Abstract. Let k \geq 0 be an integer and \alpha > 1. Let F be a family of functions meromorphic in a domain D \subset C. If {|f^(k)| / 1 + |f|^\alpha : f \in F} is locally uniformly bounded away from zero, then F is normal.

2010 Mathematics Subject Classification: Primary 30A10, 30D45.

Key words: Normal family, differential inequality.

Reference to this article: Q. Chen, S. Nevo and X. Pang: A general differential inequality of the kth derivative that leads to normality. Ann. Acad. Sci. Fenn. Math. 38 (2013), 691-695.

Full document as PDF file

doi:10.5186/aasfm.2013.3833