On nonvanishing solutions of a class of functional equations
type: Item
instance of: scholarly article
title: On nonvanishing solutions of a class of functional equations
zbMATH Open document ID: 1055.30004
published in: Rocky Mountain Journal of Mathematics
publication date: 2004-10-01T00:00:00Z
review text: Let \(\psi\) be a function holomorphic on a neighbourhood of the closed unit disk \(\mathbb{D}\subset\mathbb{C}\), such that \(\psi\) is nonnegative and increasing on \([0,1]\), \(\psi'(0)> 0\), \(\psi(1)< 1\), and \(|\varphi'(z)|\leq \psi'(| z|)\) in \(\mathbb{D}\). The author studies boundary values of holomorphic functions \(w\) in \(\mathbb{D}\) satisfying \(w(0)= 0\) and \[ \lim_{z\to\xi}| w'(z)|+ \psi(| w(z)|)= 1,\qquad \xi\in\partial\mathbb{D}. \] For example, it is shown that if \(w\) is analytic in a neighbourhood of \(\xi_0\in\partial\mathbb{D}\), then \(w(\xi_0)\neq 0\).
Mathematics Subject Classification ID: 30B30
Mathematics Subject Classification ID: 30C80
zbMATH DE Number: 2104671
author: Richard Fournier
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1216/rmjm/1181075465
OpenAlex ID: W1976210391
DOI: 10.1216/RMJM/1181075465
description: scientific article; zbMATH DE number 2104671