An alternate proof of Hall's theorem on a conformal mapping inequality
type: Item
instance of: scholarly article
title: An alternate proof of Hall's theorem on a conformal mapping inequality
zbMATH Open document ID: 0853.30010
author: R. Balasubramanian
author: Saminathan Ponnusamy
published in: Bulletin of the Belgian Mathematical Society - Simon Stevin
publication date: 1996-06-09T00:00:00Z
full work available at URL: https://eudml.org/doc/118957
review text: In this paper the authors give an alternate but simpler proof of the following theorem due to \textit{R. R. Hall} [Bull. Lond. Math. Soc. 12, 119-126 (1980; Zbl 0442.30007)]. If \(f\) is analytic for \(|z |< 1\) with \(f(0) = 0\) and is starlike of order \(1/2\). Then \[ \int^r_0 \bigl |f' (\rho e^{i \theta}) \bigr |d \rho < {\pi \over 2} \bigl |f(re^{i \theta} \bigr | \] for every \(r < 1\) and real \(\theta\).
reviewed by: V. Karunakaran
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C35
zbMATH DE Number: 885640
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 885640