Composite Holomorphic Functions and Normal Families

Xiao Bing, Wu Qifeng and Yuan Wenjun

Abstract and Applied Analysis, 2011, vol. 2011, 1-8

Abstract:

We study the normality of families of holomorphic functions. We prove the following result. Let be holomorphic functions and a family of holomorphic functions in a domain , . If and share IM for each pair and one of the following conditions holds: (1) has at least two distinct zeros for any ; (2) there exists such that has only one distinct zero and is nonconstant. Assume that is the zero of and that the multiplicities and of zeros of and at , respectively, satisfy , for all , then is normal in . In particular, the result is a kind of generalization of the famous Montel's criterion. At the same time we fill a gap in the proof of Theorem 1.1 in our original paper (Wu et al., 2010).

Date: 2011
References: Add references at CitEc
Citations:

Downloads: (external link)
http://downloads.hindawi.com/journals/AAA/2011/373910.pdf (application/pdf)
http://downloads.hindawi.com/journals/AAA/2011/373910.xml (text/xml)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:373910

DOI: 10.1155/2011/373910

Access Statistics for this article

More articles in Abstract and Applied Analysis from Hindawi
Bibliographic data for series maintained by Mohamed Abdelhakeem ().