Proceedings of the American Mathematical Society

Author(s): A. G. Aksoy; M. A. Khamsi
Journal: Proc. Amer. Math. Soc. 134 (2006), 2957-2966.
MSC (2000): Primary 47H04, 47H10, 54H25, 47H09
Posted: May 1, 2006
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Abstract: In this paper, we show that nonempty closed convex subsets of a metric tree enjoy many properties shared by convex subsets of Hilbert spaces and admissible subsets of hyperconvex spaces. Furthermore, we prove that a set-valued mapping

of a metric tree

with convex values has a selection $T: M\rightarrow M$ for which $d(T(x),T(y))\leq d_H(T^*(x),T^*(y))$ for each $x,y \in M$ . Here by

we mean the Hausdroff distance. Many applications of this result are given.

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Retrieve articles in Proceedings of the American Mathematical Society with MSC (2000): 47H04, 47H10, 54H25, 47H09

A. G. Aksoy
Affiliation: Department of Mathematics, Claremont McKenna College, Claremont, California 91711
Email: asuman.aksoy@claremontmckenna.edu

M. A. Khamsi
Affiliation: Department of Mathematical Sciences, University of Texas at El Paso, El Paso, Texas 79968-0514
Email: mohamed@math.utep.edu

DOI: 10.1090/S0002-9939-06-08555-8
PII: S 0002-9939(06)08555-8
Keywords: Metric trees, selection theorems, hyperconvex spaces
Received by editor(s): April 27, 2005
Posted: May 1, 2006
Communicated by: Jonathan M. Borwein
Copyright of article: Copyright 2006, American Mathematical Society

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