A Domain-Theoretic Bishop-Phelps theorem

Abstract

In this paper, the notion of $c$-support points of a set in a semitopological cone is introduced. It is shown that any nonempty convex Scott closed bounded set has a $c$-support point in a cancellative $bd$-cone under certain condition. We also introduce the notion of $wd$-cone and then we prove a Bishop-Phelps type theorem for $wd$-cones, especially for normed cones, under appropriate conditions. Finally, using of the Bishop-Phelps technique, we obtain a result about the fixed points of a mapping on $s$-cones.