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On Application of Differential Subordination for Certain Subclass of Meromorphically $p$-Valent Functions with Positive Coefficients Defined by Linear Operator  
 
  Authors: Waggas Galib Atshan, S.R. Kulkarni,  
  Keywords: Meromorphic functions, Differential subordination, convolution (or Hadamard product), $p$-valent functions, Linear operator, $delta$-Neighborhood, Integral representation, Linear combination, Weighted mean and Arithmetic mean.  
  Date Received: 06/01/08  
  Date Accepted: 02/05/09  
  Subject Codes:

30C45.

  
  Editors: Sever S. Dragomir,  
 
  Abstract:

This paper is mainly concerned with the application of differential subordinations for the class of meromorphic multivalent functions with positive coefficients defined by a linear operator satisfying the following:

$displaystyle - frac{z^{p+1} (L^nf(z))^{prime}}{p} prec frac{1+Az}{1+Bz}   (n in mathbb{N}_0;  z in U).$    
In the present paper, we study the coefficient bounds, $ delta$-neighborhoods and integral representations. We also obtain linear combinations, weighted and arithmetic means and convolution properties. ;


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