| 半连续函数的预不变凸性 |
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| 引用本文： | 王海英,武慧虹.半连续函数的预不变凸性[J].河南科技大学学报(自然科学版),2011,32(3):75-78,113. |
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| 作者姓名： | 王海英 武慧虹 |
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| 作者单位： | 安顺学院,数学与计算机科学系,贵州安顺561000 |
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| 基金项目： | 贵州省自然科学基金项目(20090074); 安顺学院校级课题(2010A009) |
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| 摘 要： | 在相对条件C更弱的条件C′的基础上,利用上半连续函数在紧集上必有最大值及下半连续函数满足条件H的性质,讨论了预不变凸函数与半连续函数之间的关系,排除了X是开集和集合A={λ∈0,1]:f(y+λη(x,y))≤λf(x)+(1-λ)f(y),(A)x,y ∈ X}在0,1]中的稠密性,从而简化了一些预不变凸函数性质...
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| 关 键 词： | 不变凸集 预不变凸函数 半连续函数 |
Preinvex Functions of Semi-continuous Functions |
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| WANG Hai-Ying,WU Hui-Hong.Preinvex Functions of Semi-continuous Functions[J].Journal of Henan University of Science & Technology:Natural Science,2011,32(3):75-78,113. |
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| Authors: | WANG Hai-Ying WU Hui-Hong |
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| Institution: | WANG Hai-Ying,WU Hui-Hong (Department of Mathematic & Computer Science,Anshun College,Anshun 561000,China) |
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| Abstract: | Compared with the condition C,using the conclusions that upper semi-continuous functions have maximum on compact set and lower semi-continuous functions satisfy the condition H,this paper studied the relationships between preinvex functions and semi-continuous functions under considerably weaker condition C′,being absence of the assumption that the set X was open and A={λ∈:f(y+λη(x,y))≤λf(x)+(1-λ)f(y),x,y∈X} was dense on.The proofs of property theorems about the prequasi-invex functions were simplified.Two applications in the mathematical programming problem were proposed.So the study of this type generalized convex function is improved. |
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| Keywords: | Invex set Preinvex function Semicontinuous function |
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