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Volume 8, Issue 4, Article 104 |
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Second Order Differential Subordinations of Holomorphic Mappings on Bounded Convex Balanced Domains in $C^n$
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Authors: |
Yu-Can Zhu, Ming-Sheng Liu, |
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Keywords:
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Differential subordination, biholomorphic convex mapping, convex balanced domain, Minkowski functional. |
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Date Received:
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09/11/06 |
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Date Accepted:
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04/11/07 |
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Subject Codes: |
32H02, 30C45.
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Editors: |
Gabriela Kohr, |
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Abstract: |
In this paper, we obtain some second order differential subordinations of holomorphic mappings on a bounded convex balanced domain  in  . These results imply some first order differential subordinations of holomorphic mappings on a bounded convex balanced domain in . When is the unit disc in the complex plane  , 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 .
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