Vectorial exceptional families of elements

Abstract

Let $${\mathcal{Z}}$$ be an ordered Hausdorff topological vector space with a preorder defined by a pointed closed convex cone $${C \subset {\mathcal Z}}$$ with a nonempty interior. In this paper, we introduce exceptional families of elements w.r.t. C for multivalued mappings defined on a closed convex cone of a normed space X with values in the set $${L(X, {\mathcal Z})}$$ of all continuous linear mappings from X into $${\mathcal{Z}}$$ . In Banach spaces, we prove a vectorial analogue of a theorem due to Bianchi, Hadjisavvas and Schaible. As an application, the C-EFE acceptability of C-pseudomonotone multivalued mappings is investigated.