| E-凸函数和E-拟凸函数的等价条件 |
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| 引用本文： | 韦丽兰,黄雪燕.E-凸函数和E-拟凸函数的等价条件[J].数学的实践与认识,2011,41(15). |
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| 作者姓名： | 韦丽兰 黄雪燕 |
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| 作者单位： | 1. 广西钦州学院物理与材料科学学院,广西钦州,535000
2. 广西钦州学院数学与计算机科学学院,广西钦州,535000 |
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| 摘 要： | 在更弱的连续假设下研究集合A_(x,y)={λ∈0,1]|f(λE(x)+(1-λ)E(y))≤λf(E(x))+(1-λ)f(E(y))}和集合A′_(x,y)={λ∈0,1]|f(λE(x)+(1-λ)E(y))≤max{f(E(x)),f(E(y))}}的稠密性、闭性、(弱)近似凸性,得到E-凸函数和E-拟凸函数的等价条件.
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| 关 键 词： | E-凸集 E-凸函数 E-拟凸函数 稠密 闭性 (弱)近似凸性 上(下)半连续 |
Equivalent Conditions for E-Convex Functions and E-Quasi Convex Functions |
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| WEI Li-lan,HUANG Xue-yan.Equivalent Conditions for E-Convex Functions and E-Quasi Convex Functions[J].Mathematics in Practice and Theory,2011,41(15). |
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| Authors: | WEI Li-lan HUANG Xue-yan |
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| Affiliation: | WEI Li-lan~1,HUANG Xue-yan~2 (1.Physics and Material Science College of Qinzhou University,Qinzhou 535000,China) (2.Mathematics and Computer Science College of Qinzhou University,China) |
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| Abstract: | In this paper,the density,closeness and(weak) nearly convexity of the setsA_(x,y)={λ∈0,1]|f(λE(x)+(1-λ)E(y))≤λf(E(x))+(1-λ)f(E(y))} and A'_(x,y)={λ∈0,1]|f(λE(x)+(1-λ)E(y))≤max{f(E(x),f(E(y)}} are investigated,some equivalentconditions for E-convex functions and E-quasi convex functions are derived under the weakercontinuity assumptions. |
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| Keywords: | E-convex sets E-convex functions E-quasi convex functions density closeness (weak) nearly convexity upper(lower) semi-continuous functions |
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