Sequential Farkas lemmas for convex systems

Abstract

In this paper we introduce two new versions of Farkas lemma for two kinds of convex systems in locally convex Hausdorff topological vector spaces which hold without any constraint qualification conditions. These versions hold in the limits and will be called sequential Farkas lemmas. Concretely, we establish sequential Farkas lemmas for cone-convex systems and for systems which are convex with respect to a sublinear function. The first result extends some known ones in the literature while the second is a new one.