关于与k折对称点有关的近于凸和拟凸函数族的子族(英文)  

On Subclasses of Close-to-convex and Quasi-convex Functions With Respect to k-symmetric Points

作　　者：王智刚[1,2] 高纯一[1] 刘名生[3] 廖茂新[4] 

机构地区：[1]长沙理工大学数学与计算科学学院,湖南长沙410076 [2]湖南大学数学与计量经济学院,湖南长沙410082 [3]华南师范大学数学科学学院,广东广州510631 [4]南华大学数理学院,湖南衡阳421001

出　　处：《数学进展》2009年第1期44-56,共13页Advances in Mathematics（China）

基　　金：Supported by the Scientific Research Fund of Hunan Provincial Education Department(No.08C118)of People's Republic of China.

摘　　要：本文引入了两类新的与k折对称点有关的近于凸和拟凸函数族的子族C^((k))(λ,α,β)和QC^((k))(λ,α,β).给出了这些函数族的系数不等式,积分表达式,包含和从属关系,卷积条件和覆盖定理.所得到的结果推广了一些相关文献的结果,并得到了一些新的结果.In this paper, we introduce two new subclasses C（κ） （λ,α,β） of close-to-convex functions and QC（κ） （λ,α,β） of quasi-convex functions with respect to k-symmetric points. Such results as inclusion and subordination relationships, coefficient inequalities, integral representations, convolution properties and covering theorems for these classes are proved. The results presented here would provide extensions of those given in a number of earlier works. Several other new results are also obtained.

关 键 词：解析函数族 近于凸函数族 拟凸函数族 微分从属 阿达玛卷积 κ折对称点 

分 类 号：O174.51[理学—数学]