Functions star-and convex-univalent of order \(\alpha \) with weight
type: Item
instance of: scholarly article
title: Functions star-and convex-univalent of order \(\alpha \) with weight
zbMATH Open document ID: 1159.30008
DOI: 10.1134/S1064562407060117
author: I. I. Bavrin
published in: Doklady Mathematics
publication date: 2008-12-01T00:00:00Z
review text: In this paper the author continues his previous work regarding the subclasses of the class \(Q\) of functions \(f(z)\) with \(f(0)=1\) holomorphic on the disk \(|z|<1\) and univalent with weight \(z\) on this disk. He introduces and studies the class \(M(\alpha )\) of functions \(f(z)\) with \(f(0)=1\) holomorphic on the disk \(|z|<1\) and star-univalent of order \(\alpha\) \((0<\alpha <1)\) with weight \(z\) and the class \(N(\alpha )\) of functions \(f(z)\) with \(f(0)=1\) holomorphic on the disk \(|z|<1\) and convex-univalent of order \(\alpha\) with weight \(z\). The author gives criteria for a function \(f(z)\) with \(f(0)=1\) holomorphic on the disk \(|z|<1\) to belong to the classes \(M(\alpha)\) and \(N(\alpha)\), a relationship between the functions of the classes \(M(\alpha)\) and \(N(\alpha)\), sharp bounds for the Taylor coefficients of functions from the classes \(M(\alpha)\) and \(N(\alpha)\) and sharp bounds for the moduli of a function \(f(z)\) and of the operator \(L(f(z))=f(z)+zf^{\prime}(z)\) in these classes.
reviewed by: Dorin Blezu
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 5375925
zbMATH Keywords: holomorphic and univalent functions with weight z on the unit disk
zbMATH Keywords: star-univalent functions
zbMATH Keywords: convex-univalent functions
MaRDI profile type: Publication
cites work: On the theory of univalent functions
cites work: Q4818231
description: scientific article; zbMATH DE number 5375925