A Domain-Theoretic Bishop-Phelps theorem
Functional Analysis
2019-12-25 v2
Abstract
In this paper, the notion of -support points of a set in a semitopological cone is introduced. It is shown that any nonempty convex Scott closed bounded set has a -support point in a cancellative -cone under certain condition. We also introduce the notion of -cone and then we prove a Bishop-Phelps type theorem for -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 -cones.
Cite
@article{arxiv.1412.2095,
title = {A Domain-Theoretic Bishop-Phelps theorem},
author = {Ali Hassanzadeh and Ildar Sadeqi and Asghar Ranjbari},
journal= {arXiv preprint arXiv:1412.2095},
year = {2019}
}