Canad. J. Math. 63(2011), 533-550
Printed: Jun 2011
In this paper we study the existence and uniqueness of
best proximity points of cyclic contractions as well as the convergence
of iterates to such proximity points. We take two different approaches,
each one leading to different results that complete, if not improve,
other similar results in the theory. Results in this paper stand for Banach
spaces, geodesic metric spaces and metric spaces. We also include an appendix
on CAT$(0)$ spaces where we study the particular behavior of these spaces
regarding the problems we are concerned with.
54H25 - Fixed-point and coincidence theorems [See also 47H10, 55M20]
47H09 - Contraction-type mappings, nonexpansive mappings, $A$-proper mappings, etc.