Fekete and Szego problem for a subclass of quasi-convex mappings in several complex variables  

作　　者：Qinghua XU Ting YANG Taishun LIU Huiming XU 

机构地区：[1]College of Mathematics and Information Science, Jiangxi Normal University, Nanchang 330022, China [2]Department of Mathematics, Huzhou University, Huzhou 313000, China [3]College of Mathematics, Physics and Information Engineering, Zhejiang Normal University,Jinhua 321004, China

出　　处：《Frontiers of Mathematics in China》2015年第6期1461-1472,共12页中国高等学校学术文摘·数学（英文）

基　　金：Acknowledgements This work was supported by the National Natural Science Foundation of China （Grant Nos. 11561030, 11471111, 11261022）, the Jiangxi Provincial Natural Science Foundation （Grant No. 20152ACB20002）, the Natural Science Foundation of Department of Education of Jiangxi Province （Grant No. G J J12177）, and the Zhejiang Provincial Natural Science Foundation （Grant No. Y6110053）.

摘　　要：Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that maxf∈A ｜a3 - λa22｜ ≤ max{1/3, ｜λ - 1}, ,λ ∈ C, and the estimate is sharp for each ∈. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.Let K be the familiar class of normalized convex functions in the unit disk. Keogh and Merkes proved the well-known result that maxf∈A ｜a3 - λa22｜ ≤ max{1/3, ｜λ - 1}, ,λ ∈ C, and the estimate is sharp for each ∈. We investigate the corresponding problem for a subclass of quasi-convex mappings of type B defined on the unit ball in a complex Banach space or on the unit polydisk in Cn. The proofs of these results use some restrictive assumptions, which in the case of one complex variable are automatically satisfied.

关 键 词：Fekete-Szego problem quasi-convex mappings of type A quasi-convex mappings of type B quasi-convex mappings of type C 

分 类 号：O174.13[理学—数学] O174.56[理学—基础数学]