A domain-theoretic Bishop-Phelps theorem


	Open access
	A domain-theoretic Bishop-Phelps theorem


	Fixed Point Theory, Volume 20, No. 2, 2019, 511-522, June 1st, 2019 DOI: 10.24193/fpt-ro.2019.2.33 Authors: Ali Hassanzadeh, Ildar Sadeqi and Asghar Ranjbari 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. Key Words and Phrases: s-cone, Scott topology, support point, Bishop-Phelps theorem. 2010 Mathematics Subject Classification: 46N10, 47L07, 54D10. Published on-line: June 1st, 2019. Abstract pdf Fulltext pdf Back to volume's table of contents