On quasi-convex mappings of order α in the unit ball of a complex Banach space |
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Authors: | Liu Taishun and Xu Qinghua |
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Affiliation: | (1) Department of Mathematics, Huzhou Teachers College, Huzhou, 313000, China;(2) Department of Mathematics, Jiangxi Normal University, Nanchang, 330022, China |
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Abstract: | In this paper, a class of biholomorphic mappings named quasi-convex mapping of order α in the unit ball of a complex Banach space is introduced. When the Banach space is confined to ℂ n , we obtain the relation between this class of mappings and the convex mappings. Furthermore, the growth and covering theorems of this class of mappings are given on the unit ball of a complex Banach space X. Finally, we get the second order terms coefficient estimations of the homogeneous expansion of quasi-convex mapping of order α defined on the polydisc in ℂ n and on the unit ball in a complex Banach space, respectively. Dedicated to Professor Sheng GONG on the occasion of his 75th birthday |
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Keywords: | coefficient estimation the homogeneous expansion quasi-convex mapping quasi-convex mapping of order α |
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