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On Best Proximity Points in Metric and Banach Spaces

Published online by Cambridge University Press:  20 November 2018

Rafa Espínola  and
Aurora Fernández-León
Rafa Espínola
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080-Sevilla, Spain email: [email protected]@us.es
Aurora Fernández-León
Affiliation:
Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Sevilla, 41080-Sevilla, Spain email: [email protected]@us.es
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Abstract

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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 $\text{CAT(0)}$ spaces where we study the particular behavior of these spaces regarding the problems we are concerned with.

Keywords

54H2547H09
Type
Research Article
Information
Canadian Journal of Mathematics , Volume 63 , Issue 3 , 01 June 2011 , pp. 533 - 550
Copyright
Copyright © Canadian Mathematical Society 2011

References

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