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

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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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Correspondence to M. A. Al-Thagafi.

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Open Access This article is distributed under the terms of the Creative Commons Attribution 2.0 International License (https://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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Al-Thagafi, M.A., Shahzad, N. Best Proximity Sets and Equilibrium Pairs for a Finite Family of Multimaps. Fixed Point Theory Appl 2008, 457069 (2008) doi:10.1155/2008/457069

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Keywords

  • Differential Geometry
  • Computational Biology
  • Full Article
  • Publisher Note
  • Finite Family