Open Access

Best Proximity Pairs Theorems for Continuous Set-Valued Maps

  • A. Amini-Harandi1Email author,
  • A. P. Farajzadeh2,
  • D. O'Regan3 and
  • R. P. Agarwal4
Fixed Point Theory and Applications20082008:607926

https://doi.org/10.1155/2008/607926

Received: 15 July 2008

Accepted: 16 September 2008

Published: 30 September 2008

Abstract

A best proximity pair for a set-valued map with respect to a set-valued map is defined, and a new existence theorem of best proximity pairs for continuous set-valued maps is proved in nonexpansive retract metric spaces. As an application, we derive a coincidence point theorem.

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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.