摘要
首先建立了C^n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.
In this paper, firstly, the sharp distortion theorem for a subclass of close-to- convex mappings defined in the unit polydisk of Cn is established. Furthermore, the sharp lower bound estimate of the distortion theorem for a subclass of close-to-convex mappings in the unit ball of complex Banach spaces is also established. Secondly, the sharp distortion theorem for quasi-starlike mappings in the unit ball of complex Banach spaces is given. The authors extend the distortion theorem for close-to-convex functions and starlike functions in the theory of one complex variable to higher dimensions, and give an affirmative answer to an open problem concerning distortion theorem for quasi-starlike mappings proposed by Gong Sheng.
出处
《数学年刊（A辑）》
CSCD
北大核心
2012年第1期91-100,共10页
Chinese Annals of Mathematics
基金
国家自然科学基金(No.10971063
No.11061015)
浙江省自然科学基金重大项目(No.D7080080)
浙江省创新团队项目(No.T200924)资助的项目
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
κ-折对称
Distortion theorem, Lower bound estimate, Biholomorphic convex mapping, Close-to-convex mapping, Quasi-starlike mapping, Zero of order k ＋ 1, k-Fold symmetric
