Inclusion relationships for certain subclasses of meromorphic functions defined by using the extended multiplier transformations
type: Item
instance of: scholarly article
title: Inclusion relationships for certain subclasses of meromorphic functions defined by using the extended multiplier transformations
zbMATH Open document ID: 1226.30014
DOI: 10.5402/2012/106079
published in: ISRN Mathematical Analysis
publication date: 2011-10-28T00:00:00Z
review text: Summary: Let \(\sum\) denote the class of analytic functions in the punctured unit disc \(U^{\ast} = \{z : 0 < |z| < 1\}\). Set \[ \varphi^m_{\lambda,\ell}(z) = 1/z + \sum^\infty_{k=0} [\ell + \lambda (k + 1)/\ell]^m z^k\quad (m \in \mathbb N_0; \ell > 0; \lambda \geq 0; z \in U^\ast), \] and define \(\varphi^{m,\mu}_{\lambda,\ell}\) in terms of the Hadamard product by \(\varphi^m_{\lambda,\ell} (z) \ast \varphi^{m,\mu}_{\lambda,\ell} (z) = 1/z(1 - z)^\mu\) (\(\mu > 0; z \in U^\ast\)). In this paper, we introduce several new subclasses of analytic functions defined by means of the operator \(I^m_\mu (\lambda, \ell)f(z) = \varphi^{m,\mu}_{\lambda,\ell} (z) \ast f(z)\) (\(f \in \sum; m \in \mathbb N_0; \ell > 0; \lambda \geq 0; \mu > 0\)). Inclusion properties of these classes and some applications involving integral operators are also considered.
Mathematics Subject Classification ID: 30C45
zbMATH DE Number: 5964883
author: R. M. El-Ashwah
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.5402/2012/106079
OpenAlex ID: W2063576035
Wikidata QID: Q58689741
cites work: Certain integrals for classes of p-valent meromorphic functions
cites work: Meromorphic close-to-convex functions
cites work: Q4338920
cites work: Q4936092
cites work: Q4125074
cites work: Q4740137
cites work: Q5597079
cites work: A note on certain meromorphic \(p\)-valent functions
cites work: DIFFERENTIAL SUBORDINATIONS FOR CLASSES OF MEROMORPHIC p-VALENT FUNCTIONS DEFINED BY MULTIPLIER TRANSFORMATIONS
cites work: Inclusion and argument properties for certain subclasses of meromorphic functions associated with a family of multiplier transformations
cites work: Inclusion relationships for certain subclasses of meromorphic functions associated with a family of multiplier transformations
cites work: Applications of Briot-Bouquet differential subordination to some classes of meromorphic functions
cites work: New criteria for meromorphic starlike univalent functions
cites work: Some inclusion properties of a certain family of integral operators.
cites work: Q4262846
cites work: The Noor integral and strongly starlike functions
cites work: Some properties of Noor integral operator
cites work: On integral operators
cites work: Q3308302
cites work: Differential subordinations and univalent functions
description: scientific article; zbMATH DE number 5964883