| 引用本文: | 朱健民.几类特殊多叶函数的极值点和支撑点.[J].国防科技大学学报,1990,12(3):92-97 ,91.[点击复制] |
| Zhu Jianmin.Extreme Points and Support Points of Some Special Classes of Multivalent Functions[J].Journal of National University of Defense Technology,1990,12(3):92-97 ,91[点击复制] |
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| 几类特殊多叶函数的极值点和支撑点 |
| 朱健民 |
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(系统工程与应用数学系)
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| 摘要: |
| 设S(p，α)、C(p，α)及K(p，α)分别表示α 阶的p叶星像、凸像和近于凸函数族。本文对这些函数族的支撑点和 S(p,α)的从属函数族的极值点和支撑点进行了研究，推广了Grassmann和Perera等人的结果。 |
| 关键词: 函数，复变量，极值，p叶星像，凸像，近于凸函数，极值点，支撑点 |
| DOI： |
| 投稿日期：1988-12-16 |
| 基金项目: |
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| Extreme Points and Support Points of Some Special Classes of Multivalent Functions |
| Zhu Jianmin |
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(Department of Applied Mathematics and System Engineering)
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| Abstract: |
| Let S(p，α)，C(p，α) and K(p，α) denote the classes of p-valent starlike，convex and close-to-convex functions of order α respectively. In this paper the extreme points and support points of these classes are studied and a series of results have been obtained as follows:
Theorem 1.(l) SuppS(p，α)=EHS'(p,α); (2) SuppC(p，α)=EHC(p，α);
(3) SuppK(p，α)?EHK(p，α).
Theorem 2.(1)EHs(S(p,α))={xzp/(1?yz)2(1?α)p,│x│=│y│=1}(0≤α≤1/2).
（2）Supp{s(S(p,α))J}=EHs(S(p,α))(0≤α<1/2).
Where J is a continuous linear functional on which does not have the form J(h)=ΣAnh(n)(0) for each h belonging to. |
| Keywords: function, complex,variables, extreme value, p-valent starlike,convex function,close-to-convex functions,extreme point,support points |
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