Region of variability for close-to-convex functions. II.
type: Item
instance of: scholarly article
title: Region of variability for close-to-convex functions. II.
zbMATH Open document ID: 1179.30014
published in: Applied Mathematics and Computation
publication date: 2009-10-14T00:00:00Z
review text: For a complex number \(\alpha\) with \(\Re \alpha>0\), let \(K_\phi(\alpha)\) be the class of analytic functions \(f\) in the unit disk \(\mathbb{D}\) with \(f (0)=0\) satisfying \(\Re( f'(z)/\phi'(z))>0\) in \(\mathbb{D}\), \(f'(0)/\phi'(0)=\alpha\), for some convex univalent function \(\phi\) in \(\mathbb{D}\). For any fixed \(z_0\in \mathbb{D}\) and \(\lambda \in \overline{\mathbb{D}}\), the authors determine the region of variability for \(f (z_0)\) when \(f\) ranges over the class \(K_\phi(\alpha,\lambda)\) consisting of functions \(f\in K_\phi(\alpha)\) satisfying the condition \((d/dz)(f'(z)/\phi'(z)) |_{z=0} = 2\lambda (\Re \alpha)\).
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 5614827
zbMATH Keywords: Schwarz lemma
zbMATH Keywords: starlike function
zbMATH Keywords: convex functions
zbMATH Keywords: variability region
author: Saminathan Ponnusamy
author: A. Vasudevarao
author: Hiroshi Yanagihara
reviewed by: V. Ravichandran
MaRDI profile type: Publication
full work available at URL: j.amc.2009.06.012
OpenAlex ID: W2053286405
cites work: Q4220704
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DOI: 10.1016/J.AMC.2009.06.012
description: scientific article; zbMATH DE number 5614827