Univalence for convolutions
type: Item
instance of: scholarly article
title: Univalence for convolutions
zbMATH Open document ID: 0841.30010
DOI: 10.1155/S0161171296000294
author: H. Silverman
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 1996-02-13T00:00:00Z
full work available at URL: https://eudml.org/doc/47444
review text: Let \(S\), resp. \(C\) denote the class of univalent, resp. close-to-convex functions and \(*\) the Hadamard convolution of functions analytic in the unit disk. The author proves: 1) If \(f \in S\) and \(g \in C\) then \(f*g\) is univalent in \(\{z \mid |z |< 1 - \sqrt 3\}\). The result is sharp. 2) Denote by \(r_0\) the largest value for which \(f*g\) is univalent in \(\{z \mid |z |< r_0\}\) for all \(f,g \in S\). Then \((0.8) (2 - \sqrt 3) < r_0 \leq 2 - \sqrt 3\).
reviewed by: Karl-Joachim Wirths
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C50
zbMATH DE Number: 844422
zbMATH Keywords: close-to-convex functions
zbMATH Keywords: Hadamard convolution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 844422