E-凸函数的一个等价定理

One Equivalent Theorem of E-convex Functions

E-凸函数作为凸函数的推广,近年来在凸分析、优化理论及数学规划领域中都有着重要的应用.文章首先通过定义在任意集合上函数的凸性,对E-函数的基本成分进行适当的拆分,研究得出了E-凸集与E-凸函数的相关结论;最后得出并证明了关于E-凸函数的一个等价定理,在一定程度上可丰富人们对E-凸函数的认识.

E-convex functions are the extension of convex functions and have important applications in the fields of analy- sis of convexity, optimization theory and mathematical programming in recent years. Firstly, by defining the convexity of func- tion in any set and properly partitioning the basic compositions of E-convex functions, we gave some new conclusions of E-convex sets and E-convex functions. Finally, we gained and proved one equivalent theorem of E-convex functions. All of these can, to a certain extent, enrich people＇s knowledge of E-convex function.