Univalent functions maximizing \(\text{Re}[f(\zeta_ 1)+f(\zeta_ 2)]\)
type: Item
instance of: scholarly article
title: Univalent functions maximizing \(\text{Re}[f(\zeta_ 1)+f(\zeta_ 2)]\)
zbMATH Open document ID: 0856.30016
DOI: 10.1155/S0161171296001093
author: Intisar Qumsiyeh Hibschweiler
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1997-02-04T00:00:00Z
full work available at URL: https://eudml.org/doc/47582
review text: The author studies the extremal problem. \({\mathcal R} h(\zeta_1) + {\mathcal R} h(\zeta_2) =\) maximum for \(h \in S\) and \(\zeta_1\), \(\zeta_2\) in the unit disc \(\Delta\). It is a straightforward matter to write down a corresponding variational equation and in particular to see that an extremal function suitably extended maps \(\partial \Delta\) onto a trajectory arc of the quadratic differential \[ \left( {f (\zeta_1)^2 \over f(\zeta_1) - w} + {f (\zeta_2)^2 \over f (\zeta_2) - w} \right) \left( {dw \over w} \right)^2. \] The author gives some qualitative results mostly of the form that under certain subsidiary conditions the Koebe-function and its rotations are or are not solutions of the problem.
reviewed by: James A. Jenkins
Mathematics Subject Classification ID: 30C55
Mathematics Subject Classification ID: 30C70
zbMATH DE Number: 930058
zbMATH Keywords: variational equation
zbMATH Keywords: extremal function
zbMATH Keywords: quadratic differential
zbMATH Keywords: Koebe-function
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 930058