Open Access

Best Proximity Pairs for Upper Semicontinuous 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 Applications20082008:648985

https://doi.org/10.1155/2008/648985

Received: 14 July 2008

Accepted: 27 October 2008

Published: 5 November 2008

Abstract

A best proximity pair for a set-valued map with respect to a map is defined, and new existence theorems of best proximity pairs for upper semicontinuous set-valued maps with respect to a homeomorphism are proved in hyperconvex metric spaces.

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Authors’ Affiliations

(1)
Department of Mathematics, Faculty of Basic Sciences, University of Shahrekord
(2)
Department of Mathematics, School of Science, Razi University
(3)
Department of Mathematics, College of Arts, Social Sciences and Celtic Studies, National University of Ireland
(4)
Department of Mathematical Sciences, College of Science, 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.