On properties of non-Carathéodory functions
type: Item
instance of: scholarly article
title: On properties of non-Carathéodory functions
zbMATH Open document ID: 0773.30020
author: Mamoru Nunokawa
published in: Proceedings of the Japan Academy. Series A
publication date: 1993-01-17T00:00:00Z
review text: Let \(N\) be the class of all functions that are analytic in the unit disk \(E=\{z: | z|<1\}\) and equal to 1 at \(z=0\). The author obtained the following theorem: Theorem. Let \(p(z)\in N\) and suppose that there exists a point \(z_ 0\in E\) such that \(\text{Re }p(z)>0\) for \(| z|<| z_ 0|\), \(\text{Re }p(z_ 0)=0\) and \(p(z_ 0)\neq 0\). Then we have \({z_ 0 p'(z_ 0)\over p(z_ 0)}=ik\), where \(k\) is real and \(| k|\geq 1\).
Mathematics Subject Classification ID: 30C99
zbMATH DE Number: 97951
zbMATH Keywords: Carathéodory function
MaRDI profile type: Publication
full work available at URL: pjaa.68.152
OpenAlex ID: W1964102380
cites work: Functions Starlike and Convex of Order α
cites work: Second order differential inequalities in the complex plane
DOI: 10.3792/PJAA.68.152
description: scientific article; zbMATH DE number 97951