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 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 王智刚;高纯一;刘名生;廖茂新; WANG Zhigang~ 长沙理工大学数学与计算科学学院;湖南大学数学与计量经济学院;华南师范大学数学科学学院;南华大学数理学院; (1,2,*) GAO Chunyi~(1,**) LIU Mingsheng~(3,***) LIAO Maoxin~(4,****) 1.School of Mathematics and Computing Science,Changsha University of Science and Technology,Changsha,Hunan,410076,P.R.China; 2.School of Mathematics and Econometrics,Hunan University,Cha 收稿日期: 2009-02-25 出版日期: 2009-02-25
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 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. 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,  k折对称点 Abstract：In this paper,we introduce two new subclasses C~((k))(λ,α,β)of close-to-convex functions and QC~((k))(λ,α,β)of quasi-convex functions with respect to k-symmetric points. Such results as inclusion and subordination relationships,coefficient inequalities,integral rep- resentations,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. Key words： close-to-convex functions    quasi-convex functions    differential subordination    Hadamard product    k-symmetric points
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