Certain properties of parabolic starlike and convex functions of order \(\rho\)
type: Item
instance of: scholarly article
title: Certain properties of parabolic starlike and convex functions of order \(\rho\)
zbMATH Open document ID: 1044.30005
author: D. Massart
published in: Bulletin of the Malaysian Mathematical Sciences Society. Second Series
publication date: 2004-06-14T00:00:00Z
full work available at URL: https://eudml.org/doc/50894
review text: The authors have obtained the property that \(z{f'(z)\over f(z)}\) and \(1+ z{f''(z)\over f'(z)}\) lie inside a certain parabola, with the normalization \(f(0)= 0\), \(f'(0) =1\) in the unit disc \(D= \{z\mid| z|< 1\}\). On the other hand, some particular examples of a function having the required properties are given and these examples are invariant under the particular integral operators. There is also determined the radius of uniformly convexity and the radius of uniformly starlikeness for certain functions. So obtained results are correct.
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 2074209
zbMATH Keywords: starlike functions
zbMATH Keywords: convex function
zbMATH Keywords: Hadamard product
zbMATH Keywords: subordination
reviewed by: Metin Bolcal
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2074209