中文摘要：

E-凸函数是一类十分重要的广义凸函数．提出了两类新的广义凸函数：E-伪凸函数和严格E-伪凸函数，讨论了它们和E-凸函数、E-拟凸函数以及严格E-拟凸函数之间的相互关系及在数学规划中的应用，尤其是给出了在对偶理论中的几个重要结果．所得到的结果是最近一些文献中相应结论的改进与推广．

英文摘要：

E -convexity is an important kind of generalized convexity. Two kinds of new generalized convexity functions, that is, E - Pseudo - convex function and strictly E - Pseudo - convex function, are introduced in this paper. Their relationships among E - convex function, E - Quasiconvex function and strictly E - Quasicon vex function are discussed. Subsequently, we apply these generalized convex functions to mathematical programming. Some important results in the dual problems are obtained. The conclusions improve and extend some corresponding results in references.