On growth and covering theorems of quasi-convex mappings in the unit ball of a complex banach space |
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Authors: | Zhang Wenjun and Liu Taishun |
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Institution: | 1. Department of Mathematics, Shenzhen University Normal College, Shenzhen 518060, China 2. Department of Mathematics, University of Science and Technology of China, Hefei 230026, China |
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Abstract: | A class of biholomorphic mappings named “quasi-convex mapping” is introduced in the unit ball of a complex Banach space. It
is proved that this class of mappings is a proper subset of the class of starlike mappings and contains the class of convex
mappings properly, and it has the same growth and covering theorems as the convex mappings. Furthermore, when the Banach space
is confined to ℂn, the “quasi-convex mapping” is exactly the “quasi-convex mapping of type A” introduced by K. A. Roper and T. J. Suffridge. |
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Keywords: | Banach space quasi-convex mapping growth theorem covering theorem |
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