Quasiconvexity via Two Step Functions

Quasiconvex functions are here defined and studied using a representation of these functions as generalized convex functions with respect to special classes of quasiaffine two step functions. Some of the main problems in the theory of generalized convexity aire solved for various classes of two step functions. In particular a full description is provided of generalized convex functions and generalized convex (quasiconvex) sets. The associated generalized subdifferentials are described. Applications are discussed to the solvability of certain nonlinear inequality systems involving quasiconvex functions.