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Best Proximity Pairs Theorems for Continuous Set-Valued Maps

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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Correspondence to A. Amini-Harandi.

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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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Amini-Harandi, A., Farajzadeh, A.P., O'Regan, D. et al. Best Proximity Pairs Theorems for Continuous Set-Valued Maps. Fixed Point Theory Appl 2008, 607926 (2008). https://doi.org/10.1155/2008/607926

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

Keywords

  • Differential Geometry
  • Computational Biology
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