| 刘小松;刘太顺.一类近于凸映照子族精确的偏差定理[J].数学年刊A辑,2012,33(1):91~ |
| 一类近于凸映照子族精确的偏差定理 |
| The Sharp Distortion Theorem for a Subclass of Close-to-Convex Mappings |
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| DOI： |
| 中文关键词: 偏差定理, 下界估计, 双全纯凸映照, 近于凸映照, 准星形映照, $k+1$阶零点, $k$-折对称 |
| 英文关键词:Distortion theorem, Lower bound estimate, Biholomorphic convex mapping, Close-to-convex mapping, Quasi-starlike mapping, Zero of order $k+1$, $k$-Fold symmetric |
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| 中文摘要: |
| 首先建立了$\Cn$中单位多圆柱上一类近于凸映照子族精确的偏差定理, 同时在复Banach空间单位球上也建立了该类映照精确的偏差定理的下界估计. 其次在复Banach空间单位球上建立了准星形映照精确的偏差定理. 所得结果将单复变中近于凸函数和星形函数的偏差定理推广至高维情形, 并且对龚升提出的一个公开问题给出肯定的回答. |
| 英文摘要: |
| In this paper, firstly, the sharp distortion theorem for a subclassof close-to-convex mappings defined in the unit polydisk of $\Cn$ isestablished. Furthermore, the sharp lower bound estimate of thedistortion theorem for a subclass of close-to-convex mappings in theunit ball of complex Banach spaces is also established. Secondly,the sharp distortion theorem for quasi-starlike mappings in the unitball of complex Banach spaces is given. The authors extend the distortiontheorem for close-to-convex functions and starlike functions in thetheory of one complex variable to higher dimensions, and give anaffirmative answer to an open problem concerning distortion theoremfor quasi-starlike mappings proposed by Gong Sheng. |
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