Bulletin of the Belgian Mathematical Society - Simon Stevin

Generalized CAT(0) spaces

M. A. Khamsi and S. A. Shukri

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Abstract

We extend the Gromov geometric definition of CAT(0) spaces to the case where the comparison triangles are not in the Euclidean plane but belong to a general Banach space. In particular, we study the case where the Banach space is $\ell_p$, for $p > 2$.

Article information

Source
Bull. Belg. Math. Soc. Simon Stevin Volume 24, Number 3 (2017), 417-426.

Dates
First available in Project Euclid: 27 September 2017

Permanent link to this document
https://projecteuclid.org/euclid.bbms/1506477690

Subjects
Primary: 47H09: Contraction-type mappings, nonexpansive mappings, A-proper mappings, etc.
Secondary: 46B20: Geometry and structure of normed linear spaces 47H10: Fixed-point theorems [See also 37C25, 54H25, 55M20, 58C30] 47E10

Keywords
CAT(0) spaces fixed point hyperbolic metric spaces uniformly convex uniformly Lipschitzian mapping

Citation

Khamsi, M. A.; Shukri, S. A. Generalized CAT(0) spaces. Bull. Belg. Math. Soc. Simon Stevin 24 (2017), no. 3, 417--426.https://projecteuclid.org/euclid.bbms/1506477690


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