Fixed Point Theory and Applications
Volume 2010 (2010), Article ID 213812, 19 pages
On Some Properties of Hyperconvex Spaces
1Faculty of Mathematics and Computer Science, Adam Mickiewicz University, Umultowska 87, 61-614 Poznań, Poland
2Department of Mathematics, Morgan State University, 1700 E. Cold Spring Lane, Baltimore, MD 21251, USA
3Department of Mathematics, Howard University, 2400 Sixth Street, NW, Washington, DC 20059, USA
Received 13 September 2009; Accepted 13 January 2010
Academic Editor: Mohamed A. Khamsi
Copyright © 2010 Marcin Borkowski et al. This is an open access article distributed under the
Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
We are going to answer some open questions in the theory of hyperconvex metric spaces. We prove that in complete -trees hyperconvex hulls are uniquely determined. Next we show that hyperconvexity of subsets of normed spaces implies their convexity if and only if the space under consideration is strictly convex. Moreover, we prove a Krein-Milman type theorem for -trees. Finally, we discuss a general construction of certain complete metric spaces. We analyse its
particular cases to investigate hyperconvexity via measures of noncompactness.