Open Access

Best Proximity Sets and Equilibrium Pairs for a Finite Family of Multimaps

Fixed Point Theory and Applications20082008:457069

DOI: 10.1155/2008/457069

Received: 12 May 2008

Accepted: 16 October 2008

Published: 29 October 2008

Abstract

We establish the existence of a best proximity pair for which the best proximity set is nonempty for a finite family of multimaps whose product is either an -multimap or a multimap such that both and are closed and have the KKM property for each Kakutani multimap . As applications, we obtain existence theorems of equilibrium pairs for free 1-person games as well as for free 1-person games. Our results extend and improve several well-known and recent results.

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Authors’ Affiliations

(1)
Department of Mathematics, King AbdulAziz University

Copyright

© M. A. Al-Thagafi and N. Shahzad. 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.