SOME PROPERTIES OF SEMI-$G$-PREINVEX FUNCTIONS

Abstract

In this paper, a new class of functions called semi-$G$-preinvex functions, which is generalization of semipreinvex functions and $G$-preinvex functions, is introduced. Some examples are given to show that there exist functions which are semi-$G$-preinvex functions, but are not $G$-invex functions, semipreinvex functions and $G$-preinvex functions. Furthermore, some interesting properties and characterizations of semi-$G$-preinvexity are established. Our results extend and improve the corresponding ones in the literature.