广义E-凸函数的几点新发现  

Some New Findings of Generalized E-Convex Function

作　　者：李均[1] 刘晓静[2] 

机构地区：[1]重庆师范大学数学科学学院,重庆401331 [2]重庆师范大学图书馆,重庆401331

出　　处：《重庆工商大学学报（自然科学版）》2017年第4期20-23,共4页Journal of Chongqing Technology and Business University:Natural Science Edition

基　　金：基金项目:基础科学与前沿技术研究(重点)(cstc2015jcyjBX0029)

摘　　要：广义E-凸函数在优化理论中有着重要的作用.通过对比凸函数的相关性质,得到了广义E-凸函数与凸函数的关系,对文献[5]中引理的证明举出了反例,并对E-凸函数与E-单调的等价性给出了重新证明,进一步论证了在有限维空间中,f在特定的开集E(M)上任意一点都有上界;最后,针对广义E-凸函数已有的性质和结论进行了相应的推广.The generalized E-convex function plays an important role in the optimization theory. The relationship between generalized E-convex function and convex function is obtained by comparing the correlation properties of convex functions. Then a counterexample is given for the proof of the lemma in the literature [ 5 ], and the equivalence between the E-convex function and the E-monotone is proved newly. It is further proved that f has an upper bound on a specific open set E（M） in a finite dimensional space. Finally, the properties and conclusions of the generalized E-convex function are generalized.

关 键 词：E-凸集 E-凸函数 拟-E-凸函数 拟-半-E-凸函数 E-单调 

分 类 号：O174.13[理学—数学]