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Abstract. The existence of common best proximity points for a finite commuting family of relatively nonexpansive mappings is proved. In a Hilbert space setting, the result is proved for an arbitrary family of commuting relatively nonexpansive mappings. Also the structure of the set consisting of all best proximity points of a relatively nonexpansive map is discussed.
AMS Subject Classification
(1991): 54H25, 47H10
Keyword(s):
proximal pair,
proximal normal structure,
relatively nonexpansive mapping,
fixed point,
commuting family,
metric projection
Received July 4, 2008. (Registered under 28/2008.)
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