Differential sandwich theorems for some subclasses of analytic functions associated with linear operator
type: Item
instance of: scholarly article
title: Differential sandwich theorems for some subclasses of analytic functions associated with linear operator
zbMATH Open document ID: 1122.30010
author: T. N. Shanmugam
author: A. Singaravelu
published in: Applied Mathematics and Computation
publication date: 2007-06-13T00:00:00Z
review text: The authors study on some results related to differential sandwich theorems for some subclasses of analytic functions associated with linear operator. Let \(q_{1}\) and \(q_{2}\) be univalent in \(\Delta=\{z:| z| <1\}\) with \(q_{1}(0)=q_{2}(0)=1\). The authors apply the first order differential subordination and superordination to obtain sufficient conditions for a normalised analytic functions \(f(z)\) with \(f(0)=f'(0)-1=0\) to satisfy \[ q_{1}(z)\prec\dfrac{zf'(z)}{f(z)}\prec q_{2}(z). \] The authors obtain solid 14 theorems with some applications to Carlson-Shaffer operator, Ruscheweyh and Salagean derivatives.
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 5163952
zbMATH Keywords: analytic
zbMATH Keywords: univalent
zbMATH Keywords: convex
zbMATH Keywords: extreme point
zbMATH Keywords: starlikeness
zbMATH Keywords: linear operator
reviewed by: Maslina Darus
MaRDI profile type: Publication
full work available at URL: j.amc.2006.08.144
OpenAlex ID: W1984017268
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DOI: 10.1016/J.AMC.2006.08.144
description: scientific article; zbMATH DE number 5163952