Best Proximity Pairs Theorems for Continuous Set-Valued Maps

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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Veröffentlicht in:Fixed point theory and applications (Hindawi Publishing Corporation) 2008-09, Vol.2008 (1), p.607926-607926
Hauptverfasser: Amini-Harandi, A, Farajzadeh, AP, O'Regan, D, Agarwal, RP
Format: Artikel
Sprache:eng
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Zusammenfassung: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.
ISSN:1687-1812
1687-1820
1687-1812
DOI:10.1186/1687-1812-2008-607926