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Second Order Differential Subordinations of Holomorphic Mappings on Bounded Convex Balanced Domains in $C^n$  
 
  Authors: Yu-Can Zhu, Ming-Sheng Liu,  
  Keywords: Differential subordination, biholomorphic convex mapping, convex balanced domain, Minkowski functional.  
  Date Received: 09/11/06  
  Date Accepted: 04/11/07  
  Subject Codes:

32H02, 30C45.

  
  Editors: Gabriela Kohr,  
 
  Abstract:

In this paper, we obtain some second order differential subordinations of holomorphic mappings on a bounded convex balanced domain $ Omega$ in $ mathbb{C}^n$. These results imply some first order differential subordinations of holomorphic mappings on a bounded convex balanced domain $ Omega$ in $ mathbb{C}^n$. When $ Omega$ is the unit disc in the complex plane $ mathbb{C}$, these results are just ones of Miller and Mocanu et al. about differential subordinations of analytic functions on the unit disc in the complex plane $ mathbb{C}$. ;


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