Vectorial exceptional families of elements

摘要

Let Z be an ordered Hausdorff topological vector space with a preorder defined by a pointed closed convex cone C is contained in 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, Z) of all continuous linear mappings from X into 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.