Strictly Stable Generalized Monotone Maps and Two Versions of Wald's Axiom

We consider the stable generalization of monotone maps in normed spaces. A dense subclass of s-quasimonotone maps, namely strictly s-quasimonotone maps, is introduced. For a differentiable map, strict s-quasimonotonicity of the gradient is equivalent to strict s-quasiconvexity of the underlying function. Some necessary and sufficient conditions of these maps are presented. Uses of these generalized convexity and generalized monotonicity in economics are considered. In particular, we investigate excess demand maps F in

satisfying a strong version of Wald's axiom and its weaker version on a convex cone (i.e.,

-F − F

is s-quasimonotone).