Strong differential subordination and superordination of analytic functions
type: Item
instance of: scholarly article
title: Strong differential subordination and superordination of analytic functions
zbMATH Open document ID: 1253.30025
author: M. Jeyaraman
author: T. K. Suresh
published in: Journal of Mathematical Analysis and Applications
publication date: 2011-10-24T00:00:00Z
review text: Let \(A\) be the class of functions analytic in the unit disc \(\mathbb{U}= \{z\in\mathbb{C}:|z|< 1\}\). We say that a function \(f\in A\) is subordinate to \(g\in A\) if there exists a function \(w\in A\) such that \(|w(z)|< 1\) and \(f(z)= g(w(z))\) for \(z\in \mathbb{U}\). In this case we write \(f\prec g\) or \(f(z)\prec g(z)\). Miller and Mocanu investigated many problems concerning so called ``differential subordination''. Using the methods of differential subordination the authors prove some new results. For example, the following implications are derived: \[ \Biggl|{f(z) f''(z)\over[f'(z)]^2}\Biggr|= \Biggl|\Biggl(1- {f(z) f''(z)\over [f'(z)]^2}\Biggr)- 1\Biggr|< M\Rightarrow \Biggl|{f(z)\over zf'(z)}- 1\Biggr|< M; \] \[ \Biggl|\Biggl\{\alpha\Biggl(1- {f(z) f''(z)\over [f'(z)]^2}\Biggr)+ (1-\alpha) {f(z)\over zf'(z)}\Biggr\}- 1\Biggr|< M\Rightarrow\Biggl|{f(z)\over zf'(z)}- 1\Biggr|< M. \]
reviewed by: Jan Stankiewicz
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C80
zbMATH DE Number: 5962659
zbMATH Keywords: differential subordination
zbMATH Keywords: differential superordination
zbMATH Keywords: analytic functions
zbMATH Keywords: admissible functions
MaRDI profile type: Publication
full work available at URL: j.jmaa.2011.07.016
OpenAlex ID: W1994650426
cites work: Strong differential subordination to Briot-Bouquet differential equations
cites work: STRONG DIFFERENTIAL SUBORDINATION AND APPLICATIONS TO UNIVALENCY CONDITIONS
cites work: Strong differential subordination and superordination for multivalently meromorphic functions involving the Liu–Srivastava operator
cites work: Q4936092
cites work: Subordinants of differential superordinations
cites work: Q3558385
cites work: Q3603384
cites work: Q3399375
DOI: 10.1016/J.JMAA.2011.07.016
Recommended article: Strong differential subordination and superordination for analytic functions involving certain operators
Recommended article: Differential subordination and superordination theorems for certain analytic functions
Recommended article: Q3529990
Recommended article: Q3636134
Recommended article: Q5403660
Recommended article: Q2999354
Recommended article: Q2953919
Recommended article: Q5393143
Recommended article: Q3638635
Recommended article: DIFFERENTIAL SUBORDINATION RESULTS FOR ANALYTIC FUNCTIONS
description: scientific article; zbMATH DE number 5962659