×

zbMATH — the first resource for mathematics

A note on fixed point sets in CAT(0) spaces. (English) Zbl 1101.54040
Summary: We show that the fixed point set of a quasi-nonexpansive selfmap of a nonempty convex subset of a CAT(0) space is always closed, convex and contractible. Moreover, we give a construction of a continuous selfmap of a CAT(0) space whose fixed point set is prescribed.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Ahmed, M.A.; Zeyada, F.M., On convergence of a sequence in complete metric spaces and its applications to some iterates of quasi-nonexpansive mappings, J. math. anal. appl., 274, 458-465, (2002) · Zbl 1024.47036
[2] Bridson, M.; Haefliger, A., Metric spaces of non-positive curvature, (1999), Springer-Verlag Berlin · Zbl 0988.53001
[3] Khamsi, M.A.; Kirk, W.A., An introduction to metric spaces and fixed point theory, (2001), Wiley New York · Zbl 1318.47001
[4] Kirk, W.A., Geodesic geometry and fixed point theory, (), 195-225 · Zbl 1058.53061
[5] W.A. Kirk, Geodesic geometry and fixed point theory II, in: Proceedings of the International Conference in Fixed Point Theory and Applications, Valencia, Spain, 2003, pp. 113-142 · Zbl 1083.53061
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.