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doi:10.1016/j.na.2007.04.011 
Copyright © 2007 Elsevier Ltd All rights reserved.
A concept of convergence in geodesic spaces
Received 7 November 2006;
accepted 19 April 2007.
Available online 24 April 2007.
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Abstract
A CAT(0) space is a geodesic space for which each geodesic triangle is at least as ‘thin’ as its comparison triangle in the Euclidean plane. A notion of convergence introduced independently several years ago by Lim and Kuczumow is shown in CAT(0) spaces to be very similar to the usual weak convergence in Banach spaces. In particular many Banach space results involving weak convergence have precise analogues in this setting. At the same time, many questions remain open.
Keywords: CAT(0) spaces; Δ-convergence; Weak convergence; Fixed points
Mathematical subject codes: 54H25; 54E40; 05C05
Article Outline
- 1. Introduction
- 2. Preliminary remarks
- 3. Basic properties of Δ-convergence
- 4. A four point condition
- 5. LANE mappings
- 6. J-type mappings
- 7. Concluding remarks
- References
