Differential subordination and Bazilevič functions
type: Item
instance of: scholarly article
title: Differential subordination and Bazilevič functions
zbMATH Open document ID: 0859.30024
DOI: 10.1007/BF02880363
author: Saminathan Ponnusamy
published in: Proceedings of the Indian Academy of Sciences. Mathematical Sciences
publication date: 1996-07-15T00:00:00Z
review text: Let \(p\), \(\lambda\), \(h\) and \(\phi\) be analytic functions in the unit disc \(\Delta\). In this paper, the author proves that, under suitable assumptions on the above functions, the following relation holds: \(p(z)+ \lambda(z)zp'(z)\prec h(z)\) implies \(p(z)\prec \phi(z)\prec h(z)\) for \(z\in\Delta\), where \(\prec\) denotes the subordination of functions. Basing himself on this result he proves a sufficient condition for an analytic function to be starlike in \(\Delta\). These results are some extensions of the classical result of Sakaguchi and Libera.
Mathematics Subject Classification ID: 30C80
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 903349
zbMATH Keywords: Bazilevič functions
zbMATH Keywords: Sakaguchi
zbMATH Keywords: Libera
reviewed by: Stanislaw Walczak
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf02880363
OpenAlex ID: W2020139406
description: scientific article; zbMATH DE number 903349