Geometric properties of solutions of a class of differential equations
type: Item
instance of: scholarly article
title: Geometric properties of solutions of a class of differential equations
zbMATH Open document ID: 1069.34132
publication date: 2005-03-08T00:00:00Z
review text: The paper is concerned with a few geometric properties of the solutions of the second order linear differential equations \[ w''(z) + a(z) w'(z) + b(z) w(z) = 0, \] with coefficients analytic in the open unit disk. Under several boundedness assumptions on the coefficients, the authors obtain estimations of \(\Re \frac{zw'(z)}{w(z)}\) or \(\frac{zw'(z)}{w(z)}\). These results then imply, in different situations, the solutions to be starlike. The proof is based on an earlier result due to \textit{H. Saitoh} [Ann. Univ. Mariae Curie-Sklodowska, Sect. A 53, 209--216 (1999; Zbl 0984.30007)].
Mathematics Subject Classification ID: 34M10
Mathematics Subject Classification ID: 33C15
zbMATH DE Number: 2142419
zbMATH Keywords: differential equations
zbMATH Keywords: analytic functions
zbMATH Keywords: starlike functions
author: Shigeyoshi Owa
author: Hitoshi Saitoh
author: H. M. Srivastava
author: Rikuo Yamakawa
reviewed by: Yuefei Wang
MaRDI profile type: Publication
full work available at URL: j.camwa.2004.06.017
OpenAlex ID: W1979730768
Wikidata QID: Q115359631
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DOI: 10.1016/J.CAMWA.2004.06.017
published in: Computers & Mathematics with Applications
description: scientific article; zbMATH DE number 2142419