On best proximity points in metric and Banach spaces

Details On best proximity points in metric and Banach spaces On best proximity points in metric and Banach spaces

2009-11-27

arxiv.org/abs/0911.5263v1

Mathematics

Functional Analysis

17 pages. Accepted for publication in the Canadian Mathematical Bulletin

Scientific paper

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 do it from two different approaches, leading each one of them to different results which 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.

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