Generalized CAT(0) spaces. (English) Zbl 1478.54017

Khamsi, M. A.; Shukri, S. A.

Bull. Belg. Math. Soc. - Simon Stevin 24, No. 3, 417-426 (2017).

Summary: 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 \(p > 2\).

MSC:

54E35	Metric spaces, metrizability
54E15	Uniform structures and generalizations
54E40	Special maps on metric spaces
54H25	Fixed-point and coincidence theorems (topological aspects)

Keywords:

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