A dual generalization of convex functions

Abstract

As it is well known, the convexity property of a function may be described by the quasiconvexity property of all "the dual perturbations" of this function. If we consider the "dual perturbation" only in a subset $M\subset X^{\ast}$ we obtain a general class of functions called $M$-convex. In this paper we establish some special properties and a continuity theorem of this new type of functions