| 集合的E-凸性与函数的E-凸性及拟E-凸性 |
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| 引用本文： | 吴欧. 集合的E-凸性与函数的E-凸性及拟E-凸性[J]. 江汉大学学报(自然科学版), 2006, 34(4): 17-19 |
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| 作者姓名： | 吴欧 |
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| 作者单位： | 重庆师范大学,数学与计算机科学学院,重庆,400047 |
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| 摘 要： | 给出了集合的E-凸性的一些新的判别准则,同时,对Chen的文章"Somepropertiesofsemi-E-convexfunctions"中的定理12作了进一步讨论,简化了Chen的证明,同时给出了一个等价条件.此外,证明了函数的拟半E-凸性及相应水平集之间的等价关系,最后,对王建勇等文章“E-拟凸函数”中的命题4给出了一个反例.
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| 关 键 词： | E-凸集 E-凸函数 半E-凸性 拟半E-凸性 水平集 |
| 文章编号： | 1673-0143（2006）04-0017-03 |
| 收稿时间： | 2006-05-29 |
| 修稿时间： | 2006-05-29 |
E-convexity of Sets, Semi-E-convexity and Quasi-semi-E-convexity of Functions |
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| WU Ou. E-convexity of Sets, Semi-E-convexity and Quasi-semi-E-convexity of Functions[J]. Journal of Jianghan University(Natural Sciences), 2006, 34(4): 17-19 |
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| Authors: | WU Ou |
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| Abstract: | Firstly, gives some new criterias of E-convexity of sets. At the same time, further discusses theorem 12 of article "Some properties of semi-E-convex functions"writen by Chen, sim- plify the proof of Chen. Meanwhile givesanother equivalent condition. Furthermore, the equivalent relation between quasi-semi-E-convexity of functions and corresponding level sets is proved. At the end, a counterexample with proposition 4 of article "E-quasi-convex function "by Wang Jianyong is given. |
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| Keywords: | E-convex sets E-convex function semi-E-convexity quasi-semi-E-convexcity level sets |
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