A third-order differential equation and starlikeness of a double integral operator
type: Item
instance of: scholarly article
title: A third-order differential equation and starlikeness of a double integral operator
zbMATH Open document ID: 1207.30012
DOI: 10.1155/2011/901235
author: See Keong Lee
author: K. G. Subramanian
author: Rosihan M. Ali
author: Anbhu Swaminathan
published in: Abstract and Applied Analysis
publication date: 2011-02-09T00:00:00Z
full work available at URL: https://eudml.org/doc/224493
review text: Summary: Functions \(f(z)=z+\sum_{n=2}^\infty a_n z^n\) that are analytic in the unit disk and satisfy the differential equation \(f'(z)+\alpha z f''(z)+\beta z^2 f'''(z)=g(z)\) are considered, where \(g\) is subordinated to a normalized convex univalent function \(h\). These functions \(f\) are given by a double integral operator of the form \[ f(z)=\int_0^1\int_0^1 G(z t^\mu s^\nu) t^{-\mu} s^{-\nu} ds dt \] with \(G'\) subordinated to \(h\). The best dominant to all solutions of the differential equation is obtained. Starlikeness properties and various sharp estimates of these solutions are investigated for particular cases of the convex function \(h\).
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 5848832
zbMATH Keywords: starlike function
Wikidata QID: Q58654515
MaRDI profile type: Publication
OpenAlex ID: W2091392594
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description: scientific article; zbMATH DE number 5848832