Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator
type: Item
instance of: scholarly article
title: Double subordination preserving properties for a new generalized Srivastava-Attiya integral operator
zbMATH Open document ID: 1318.30035
author: Teodor Bulboacă
author: Jugal Kishore Prajapat
published in: Chinese Annals of Mathematics. Series B
publication date: 2012-12-06T00:00:00Z
review text: Let \(\mathcal A\) be the class of analytic functions \(f\) in the unit disk \(U\) of the form \(f(z)=z+\sum_{n=2}^\infty a_nz^n\), and, for \(\lambda,\mu,s\in\mathbb C\) and \(\nu, a\in\mathbb C\setminus\mathbb Z^-\), let \(\mathcal J_{\lambda,\mu;\nu}^{s,a}:\mathcal A\to\mathcal A\) be the linear operator defined by \[ \mathcal J_{\lambda,\mu;\nu}^{s,a}f(z)=z+\sum_{n=2}^\infty\frac{(\lambda+1)_{n-1}(\mu+1)_{n-1}}{(\nu+1)_{n-1}n!}\left(\frac{1+a}{n+a}\right)^sa_nz^n, \;z\in U. \] This operator, named by the authors the ``Srivastava-Attiya operator'', is the object of the paper. Two results concerning subordination and superordination with such kind of operators are given, and a lot of consequences are also found, some of them involving generalized hypergeometric functions.
reviewed by: Eugen Drăghici
Mathematics Subject Classification ID: 30C45
Mathematics Subject Classification ID: 30C80
zbMATH DE Number: 6112849
zbMATH Keywords: star-like functions
zbMATH Keywords: convex functions
zbMATH Keywords: differential subordination
zbMATH Keywords: generalized hypergeometric functions
MaRDI profile type: Publication
full work available at URL: s11401-012-0722-3
OpenAlex ID: W2021223423
cites work: Subordination and superordination of the Liu-Srivastava linear operator on meromorphic functions
cites work: Differential subordination and superordination of analytic functions defined by the multiplier transformation
cites work: Convex and Starlike Univalent Functions
cites work: Q4385553
cites work: A class of superordination-preserving integral operators
cites work: Starlike and Prestarlike Hypergeometric Functions
cites work: Argument estimates of certain analytic functions defined by a class of multiplier transformations.
cites work: Some inclusion properties of a certain family of integral operators.
cites work: Q5323994
cites work: Q3562189
cites work: Q5696445
cites work: The Hardy space of analytic functions associated with certain one-parameter families of integral operators
cites work: Q4936092
cites work: Subordinants of differential superordinations
cites work: Subordination-Preserving Integral Operators
cites work: Some subclasses of analytic and spiral-like functions of complex order involving the Srivastava–Attiya integral operator
cites work: Univalent and Starlike Generalized Hypergeometric Functions
cites work: Applications of Srivastava-Attiya operator to the classes of strongly starlike and strongly convex functions
cites work: NEW SUFFICIENT CONDITIONS FOR STARLIKENESS OF ANALYTIC FUNCTIONS INVOLVING A FRACTIONAL DIFFERINTEGRAL OPERATOR
cites work: An integral operator associated with the Hurwitz–Lerch Zeta function and differential subordination
cites work: Series associated with the zeta and related functions
cites work: Integral and computational representations of the extended Hurwitz–Lerch zeta function
cites work: A family of integral operators preserving subordination and superordination
DOI: 10.1007/S11401-012-0722-3
description: scientific article; zbMATH DE number 6112849