E-凸函数的一个等价定理

摘要

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.%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。