Subclasses of regular and schlicht functions with fixed coefficients
type: Item
instance of: scholarly article
title: Subclasses of regular and schlicht functions with fixed coefficients
zbMATH Open document ID: 0733.30013
DOI: 10.1007/BF01058944
author: V. A. Pokhilevich
published in: Ukrainian Mathematical Journal
publication date: 1991-01-01T00:00:00Z
review text: Let \(\alpha\),\(\beta\in [0,1)\), \(\theta\in [0,2\pi]\), n,k\(\in N\) be fixed numbers and let \(E=\{z:| z| <1\}\). Denote by \(P(2\alpha (1- \beta)e^{i\theta},n,n+k)\) the class of functions q holomorphic in E, satisfying in the disc the condition Re q(z)\(>\beta\) and having the form \[ q(z)=1+2\alpha (1-\beta)e^{i\theta}z^ n+2p_{n+k}z^{n+k}+...,\quad z\in E. \] In the paper, the author determines in this class the domain of values of the functional \(I_ 0(q)=q(z)\), \(z\in E\)- fixed. He also gives a few applications of the above-mentioned result.
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 4212391
zbMATH Keywords: domain of values of a functional
MaRDI profile type: Publication
cites work: Close-to-convex schlicht functions
cites work: Q4777581
cites work: Q5547758
cites work: Q3957190
full work available at URL: https://doi.org/10.1007/bf01058944
OpenAlex ID: W2092074388
description: scientific article; zbMATH DE number 4212391