On differential subordinations for a class of analytic functions defined by a linear operator
type: Item
instance of: scholarly article
title: On differential subordinations for a class of analytic functions defined by a linear operator
zbMATH Open document ID: 1108.30009
DOI: 10.1155/S0161171204309208
author: H. Silverman
author: S. Sivaprasad Kumar
author: K. G. Subramanian
author: V. Ravichandran
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-25T00:00:00Z
full work available at URL: https://eudml.org/doc/53057
review text: Let \({\mathcal A}\) be the class of functions \(f(z)=z+\sum_{k=2}^\infty a_kz^k\) that are analytic in the unit disc \({\mathcal U}=\{z:| z| <1\}.\) In this paper the authors study the following linear operator \[ L(a,c)f(z) := z+ \sum_{n=1}^\infty \frac{(a)_n}{(c)_n}\;a_{n+1}\;z^{n+1} \] and give sufficient conditions for functions to satisfy the subordinations \[ \frac{L(a,c)f(z)}{L(a+1,c)f(z)}\prec q(z), \quad\left( \frac{L(a,c)f(z)}{L(a+1,c)f(z)}\right)^\beta \prec q(z), \] and \[ \left( \frac{L(a,c)f(z)}{z}\right)^\beta \prec q(z), \quad \frac{z}{L(a+1,c)f(z)}\prec q(z). \] Here \(f(z), q(z)\in{\mathcal A},\) \(``\prec"\) denotes the usual subordination and \((\chi)_n\) is the shifted factorial. Also, some applications of the obtained results are given and comparison with previous known results is done.
reviewed by: Nikola Tuneski
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C80
zbMATH DE Number: 2171586
zbMATH Keywords: analytic function
zbMATH Keywords: differential subordination
zbMATH Keywords: linear operator
zbMATH Keywords: sufficient condition
MaRDI profile type: Publication
OpenAlex ID: W2101247208
description: scientific article; zbMATH DE number 2171586