Open Access

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

  • A. Amini-Harandi1Email author,
  • A. P. Farajzadeh2,
  • D. O'Regan3 and
  • R. P. Agarwal4
Fixed Point Theory and Applications20082008:543154

https://doi.org/10.1155/2008/543154

Received: 8 October 2008

Accepted: 9 December 2008

Published: 21 December 2008

Abstract

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.

Publisher note

To access the full article, please see PDF.

Authors’ Affiliations

(1)
Department of Mathematics, University of Shahrekord
(2)
Department of Mathematics, Razi University
(3)
Department of Mathematics, National University of Ireland
(4)
Department of Mathematical Sciences, Florida Institute of Technology

Copyright

© 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.