Order preserving functions and generalized convexity

In order to better understand the monotonicity properties which characterize the gradient of pseudoconvex and quasi convex funzions, psedomonotonicity and quasi monotonicity can be introduced. A quite different approach is proposed in this paper, by defining new order relations, whose preservation leads precisely to several kinds of pseudoconvexity and quasi convexity. Some general properties of order preservation are proved; they are useful to state necessary and sufficient conditions of monotonicity for particular orders related with generalized convexity. © 1991 Springer-Verlag.