A Domain-Theoretic Bishop-Phelps theorem

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 B...

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Bibliographic Details
Main Authors Hassanzadeh, Ali, Sadeqi, Ildar, Ranjbari, Asghar
Format Journal Article
LanguageEnglish
Published 05.12.2014
Subjects
Mathematics - Functional Analysis
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Summary: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.
DOI:10.48550/arxiv.1412.2095