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sharp Growth Theorems and coefficient bounds for Starlike Mappings in Several Complex Variables

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Chinese Annals of Mathematics,Series B 2008年第4期29卷 353-368页

作者： Hidetaka HAMADA Tatsuhiro HONDA Faculty of Engineering Kyushu Sangyo University Department of Architectural Engineering Hiroshima Institute of Technology

Let B be the unit ball in a complex Banach space. Let S^＊k＋1（B） be the family of normalized starlike mappings f on B such that z = 0 is a zero of order k ＋ 1 of f（z） - z. The authors obtain sharp growth and cov... 详细信息

关键词： sharp coefficient bound sharp covering theorem sharp growth theorem Starlike mapping Zero of order k

On the Fekete and Szego Problem for Starlike Mappings of Order α

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Acta Mathematica Sinica,English Series 2017年第4期33卷 554-564页

作者： Qing Hua XU Fang FANG Tai Shun LIU College of Mathematics and Information Science JiangXi Normal University Nanchang 330022 P. R. China Department of Mathematics Huzhou University Huzhou 313000 P. R. China

Let Sα*be the familiar class of normalized starlike functions of order α in the unit disk. In this paper, we establish the Fekete and Szeg? inequality for the class Sα*, and then we generalize this result to the un... 详细信息

关键词： Fekete–Szego problem starlike mappings of order α sharp coefficient bound

Fekete and Szeg problem in one and higher dimensions

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Science China Mathematics 2018年第10期61卷 1775-1788页

作者： Qinghua Xu Taishun Liu Xiaosong Liu School of Science Zhejiang University of Science and Technology Hangzhou 310023 China Department of Mathematics Huzhou University Huzhou 313000 China School of Mathematics and Computation Science Lingnan Normal University Zhanjiang 524048 China

In this paper, we establish the Fekete and Szego inequality for a class of holomorphic functions in the unit disk, and then we extend this result to a class of holomorphic mappings on the unit ball in a complex Banach... 详细信息

关键词： Fekete and Szego problem Bieberbach conjectures in several complex variables subclasses ofstarlike mappings sharp coefficient bound

On the coefficient Inequality for A Subclass of Starlike Mappings in Several Complex Variables

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Chinese Quarterly Journal of Mathematics 2018年第1期33卷 98-110页

作者： GUO Sheng-ti XU Qing-hua College of Mathematics and Information Science JiangXi Normal JiangXi Normal University NanChang 330022 China School of Science Zhejiang University of Science and Technology Hangzhou 310023 China

Let S~* be the familiar class of normalized univalent functions in the unit *** [9], Keogh and Merkes proved that for a function f(z) = z +∑k=2∞ a_kz^k in the class S~*,then |a_3-λa_2~2| ≤ max{1, |3-4λ|}, λ∈ C. In this article, we investigate the corresponding problem for the subclass of starlike mappings defined on the unit ball in a complex Banach space, on the unit polydisk in Cnand the bounded starlike circular domain in C~■, respectively.

关键词： Fekete-Szego problem Subclass of starlike mappings sharp coefficient bound