广义预不变凸函数和单调映射

On Generalized Preinvex Functions and Monotonicity

广义预不变凸函数是凸函数的重要推广函数,在数学规划中有许多应用.本文在给出一类广义预不变凸函数——α-(预)不变凸函数、伪α-预不变凸函数等定义的基础上,研究了它们之间的关系及其和单调映射间的联系.

Generalized preinvex function, which is one kind of important function of convex functions, has many application in mathematical programming. In this paper, a general class of preinvex function, α-preinvex（ α-invex）function and Pseudo α-preinvex function, is presented. We study some properties of these function. In particular, we discuss the relation between these functions and monotonicities under some suitable conditions.