A class of functions, called semistrictly preinvex functions is defined. This is a generalization of the class of preinvex functions introduced by T. Weir
and B. Mond
[J. Math. Anal. Appl. 136, No. 1, 29-38 (1988; Zbl 0663.90087
)] and by T. Weir
and V. Jeyakumar
[Bull. Aust. Math. Soc. 38, No. 2, 177-189 (1988; Zbl 0639.90082
)]. It is shown that for the functions of this new class any local minimizer is global. A relationship between preinvex functions and semistrictly preinvex functions and some properties of semistrictly preinvex functions are also given.