Semistrictly Preinvex Functions1

A new class of functions, termed semistrictly preinvex functions, is introduced in this paper. Some properties of semistrictly preinvex functions are discussed. In particular, the relationship between semistrictly preinvex functions and preinvex functions is investigated. Some characterization properties of semistrictly preinvex functions are derived under a lower semicontinuous condition, and a gradient property of semistrictly preinvex functions is obtained.