Abstract: A new class of important generalized convex functions-prequasi-invex function is further discussed.To improve research on the generalized convex function,some new characteristics of the prequasi-invex function are figured out by means of the cographical set of function (E (f)={ (x,α):x∈K,α∈R,f (x)≤α}) and-invex set,and its two applications in the mathematical programming problem are proposed.So the study of this type generalized convex function becomes further now.

Key words: invex set, preinvex functions, strongly preinvex functions, new characters, application

摘要： 对一类新的广义凸函数-强预不变凸函数作了进一步研究。首先给出例子说明了此类广义凸函数的存在性,然后利用强η-不变凸集和函数的上图(E(f)={(x,α):x∈K,α∈R,f(x)≤α})得到了强预不变凸函数的几个重要性质,并用另一方法给出它的一个判别定理的简化证明,最后还给出了强预不变凸函数在数学规划问题中的一个重要应用,从而完善了对此类广义凸函数的研究。

关键词: 不变凸集, 预不变凸函数, 强预不变凸函数, 新性质, 应用