Normal criterion concerning shared values
type: Item
instance of: scholarly article
title: Normal criterion concerning shared values
zbMATH Open document ID: 1253.30046
DOI: 10.1155/2012/312324
author: Wei Chen
author: Yingying Zhang
author: Jiwen Zeng
author: Honggen Tian
published in: Journal of Applied Mathematics
publication date: 2012-11-15T00:00:00Z
review text: Summary: We prove the following normality criterion: Let \(F\) be a family of meromorphic functions in a domain \(D\) whose zeros have multiplicity at least 2. Assume that there exists nonzero complex numbers \(b_f\), \(c_f\) depending on \(f\) satisfying: (i) \(b_f/c_f\) is a constant; (ii) \(\min \{\sigma(0, b_f), \sigma(0, c_f), \sigma(b_f, c_f)\} \geq m\) for some \(m > 0\); (iii) if \((1/c^{k-1}_f)(f')^k(z) + f(z) \neq b^k_f/c^{k-1}_f\) or \((1/c^{k-1}_f)(f')^k(z) + f(z) = b^k_f/c^{k-1}_f\) then \(f(z) = b_f\). Then \(F\) is normal.
Mathematics Subject Classification ID: 30D45
Mathematics Subject Classification ID: 30D35
zbMATH DE Number: 6106173
zbMATH Keywords: normality criterion
zbMATH Keywords: meromorphic functions
zbMATH Keywords: shared values
Wikidata QID: Q58906624
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2012/312324
OpenAlex ID: W2115946824
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description: scientific article; zbMATH DE number 6106173