A generic approach to approximate efficiency and applications to vector optimization with set‐valued maps

In this paper we focus on approximate minimal points of a set in Hausdorff locally convex spaces. Our aim is to develop a general framework from which it is possible to deduce important properties of these points by applying simple results. For this purpose we introduce a new concept of ϵ‐efficient point based on set‐valued mappings and we obtain existence results and properties on the behavior of these approximate efficient points when ϵ is fixed and by considering that ϵ tends to zero. Finally, the obtained results are applied to vector optimization problems with set‐valued mappings.