半(p,r)-预不变凸函数

Semi (p,r)-Preinvex Functions

首先,定义了一类广义凸集——半p-不变凸集,在此基础之上,利用半预不变凸函数和(p,r)-预不变凸函数,定义了一类新的广义凸函数——半(p,r)-预不变凸函数,并举例说明了它既是半预不变凸函数又是(p,r)-预不变凸函数的真推广,从而是熟知的凸函数和不变凸函数的推广形式.接着,讨论了它的一些有用性质,研究了它在极值问题中的应用.其结果具有一般性,推广了许多涉及不变凸函数,半预不变凸函数和(p,r)-预不变凸函数的文献的结论.

First, a class of generalized convex set——semi p-invex set is defined and based on this, by using semi-preinvexity functions and （p, r）-preinvexity functions, a class of new generalized convex functions called semi （p, r）-preinvexity functions are defined. It is showed with the aid of some examples that it is real generalization of the semi-preinvexity functions and （p, r）-preinvexity functions, thus it is the generalization of well known convexity functions and invexity functions. Then, some properties and its application in extreme problem are discussed. The work generalizes many results involving invex functions, semi- preinvexity functions and （p, r）-preinvexity functions.