Some properties of certain meromorphically multivalent functions associated with the extended multiplier transformation

2010 ◽  
Vol 16 (2) ◽  
Author(s):  
M. K. Aouf ◽  
A. Shamandy ◽  
R. M. El-Ashwah ◽  
E. E. Ali
Author(s):  
Deepali Khurana ◽  
Raj Kumar ◽  
Sibel Yalcin

We define two new subclasses, $HS(k, \lambda, b, \alpha)$ and \linebreak $\overline{HS}(k, \lambda, b, \alpha)$, of univalent harmonic mappings using multiplier transformation. We obtain a sufficient condition for harmonic univalent functions to be in $HS(k,\lambda,b,\alpha)$ and we prove that this condition is also necessary for the functions in the class $\overline{HS} (k,\lambda,b,\alpha)$. We also obtain extreme points, distortion bounds, convex combination, radius of convexity and Bernandi-Libera-Livingston integral for the functions in the class $\overline{HS}(k,\lambda,b,\alpha)$.


1995 ◽  
Vol 18 (3) ◽  
pp. 463-467
Author(s):  
Nak Eun Cho ◽  
Ji A. Kim

The object of the present paper is to introduce a new class∑n(α)of meromorphic functions defined by a multiplier transformation and to investigate some properties for the class∑n(α)Further we study integrals of functions in∑n(α).


2014 ◽  
Vol 2014 ◽  
pp. 1-12
Author(s):  
M. P. Jeyaraman ◽  
T. K. Suresh

The main object of the present paper is to investigate several interesting subordination properties and a sharp inclusion relationship for certain subclass of multivalent analytic functions, which are defined here by the generalized multiplier transformation. Relevant connections of the results which are presented in this paper with various known results are also considered.


2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
F. Ghanim ◽  
M. Darus

Motivated by a multiplier transformation and some subclasses of meromorphic functions which were defined by means of the Hadamard product of the Cho-Kwon-Srivastava operator, we define here a similar transformation by means of the Ghanim and Darus operator. A class related to this transformation will be introduced and the properties will be discussed.


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