A first order characterization of generalized monotonicity

It is shown that pseudomonotone and quasimonotone maps can be characterized by a first order property provided they are regular. This result extends the well known characterization of nonvanishing generalized monotone maps to an essentially larger class. The paper supplements a recent contribution by Crouzeix and Ferland and solves a related open problem concerning homogeneous excess demand functions which occur in general equilibrium theory.