On the sets of values of the initial coefficients in class of typically real functions
type: Item
instance of: scholarly article
title: On the sets of values of the initial coefficients in class of typically real functions
zbMATH Open document ID: 1004.30011
DOI: 10.1023/A:1015464026397
author: E. G. Goluzina
published in: Journal of Mathematical Sciences (New York)
publication date: 2002-08-29T00:00:00Z
review text: Let \(T\) denote the class of holomorphic and typically real functions \(f(z)=z+c_2z^2+c_3z^3+\dots\) in the unit disk \(\mathbb D=\{z:|z|<1\}\) (i.e. \(\operatorname {Im}f(z)\operatorname {Im}z\geq 0\), \(z\in\mathbb D\)). For given fixed \(z_1\in\mathbb D\) and \(w_1\in\{w:w=f(z_1),\;f\in T\}\) the author determines the exact set of values of \(\{c_2\}\) and of \(\{c_3\}\) within the class \(T\). The Carathéodory inequalities for functions with positive real part are used for the proof. All extremal functions are determined.
reviewed by: Jan Szynal
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 1777275
zbMATH Keywords: typically real functions
MaRDI profile type: Publication
full work available at URL: a:1015464026397
OpenAlex ID: W133072159
description: scientific article; zbMATH DE number 1777275