On properties of preinvex functions

Abstract

We consider in this paper the class of preinvex functions introduced by T. Weir and co-workers (1988, J. Math. Anal. Appl.136, 29-38; 1988, Bull. Austral. Math. Soc.38, 177-189). Under semi-continuity conditions, a determination of the satisfaction of preinvexity for a function can be achieved via an intermediate-point preinvexity check. A characterization of a preinvex function in terms of its relationship with an intermediate-point preinvexity and prequasi-invexity is provided. © 2001 Academic Press.