Two new criteria for normal families
type: Item
instance of: scholarly article
title: Two new criteria for normal families
zbMATH Open document ID: 1096.32001
DOI: 10.1007/BF03321086
author: Eleanor Clifford
published in: Computational Methods and Function Theory
publication date: 2006-03-10T00:00:00Z
review text: The author considers a family \(\mathbf F\) of meromorphic functions defined on the domain \(\Omega\) and shows when the set \(\{f'/f \in \mathbf F\}\) is a normal family. The following theorems are the main results of this paper. Theorem 1. Let \(k \geq 2\) and \(a_0, \ldots, a_{k-1}\) be analytic functions on \(\Omega.\) If \(f\) and \(L(f):= f^{(k)} + a_{k-1} f^{(k-1)} + \ldots + a_1 f' + a_0 f\) are the functions without zeros on \(\Omega\) for each \(f \in \mathbf F\) then \(\{f'/f \in \mathbf F\}\) is a normal family on \(\Omega.\) Theorem 2. Let \(k \geq 2\) and \(a_0, \ldots, a_{k-1}\) be meromorphic functions on \(\Omega.\) If \(f,\) \(f'\) and \(L(f)\) are the functions without zeros on \(\Omega\) for each \(f \in \mathbf F\) then \(\{f'/f \in \mathbf F\}\) is a normal family on \(\Omega.\)
Mathematics Subject Classification ID: 32A19
Mathematics Subject Classification ID: 32A20
zbMATH DE Number: 5011336
zbMATH Keywords: analytic function
zbMATH Keywords: meromorphic function
zbMATH Keywords: normal family
reviewed by: P. Z. Agranovich
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 5011336