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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.

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
Full Text: DOI
[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
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