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  • Research Article
  • Open Access

Coincidence Point, Best Approximation, and Best Proximity Theorems for Condensing Set-Valued Maps in Hyperconvex Metric Spaces

  • 1Email author,
  • 2,
  • 3 and
  • 4
Fixed Point Theory and Applications20082008:543154

  • Received: 8 October 2008
  • Accepted: 9 December 2008
  • Published:


In hyperconvex metric spaces, we first present a coincidence point theorem for condensing set-valued self-maps. Then we consider the best approximation problem and the best proximity problem for set-valued mappings that are condensing. As an application, we derive a coincidence point theorem for nonself-condensing set-valued maps.


  • Point Theorem
  • Differential Geometry
  • Approximation Problem
  • Computational Biology
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Authors’ Affiliations

Department of Mathematics, University of Shahrekord, Shahrekord, 88186-34141, Iran
Department of Mathematics, Razi University, Kermanshah, 67149, Iran
Department of Mathematics, National University of Ireland, Galway, Ireland
Department of Mathematical Sciences, Florida Institute of Technology, Melbourne, FL 32901, USA


© A. Amini-Harandi et al. 2008

This article is published under license to BioMed Central Ltd. 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.