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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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A selection theorem in metric trees
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by A. G. Aksoy and M. A. Khamsi PDF
Proc. Amer. Math. Soc. 134 (2006), 2957-2966 Request permission

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 $T^*$ of a metric tree $M$ 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 $d_H$ we mean the Hausdroff distance. Many applications of this result are given.
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Additional Information
  • A. G. Aksoy
  • Affiliation: Department of Mathematics, Claremont McKenna College, Claremont, California 91711
  • MR Author ID: 24095
  • 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
  • Received by editor(s): April 27, 2005
  • Published electronically: May 1, 2006
  • Communicated by: Jonathan M. Borwein
  • © Copyright 2006 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 134 (2006), 2957-2966
  • MSC (2000): Primary 47H04, 47H10, 54H25, 47H09
  • DOI: https://doi.org/10.1090/S0002-9939-06-08555-8
  • MathSciNet review: 2231620