Dhompongsa, S.; Kirk, W. A.; Panyanak, B. Nonexpansive set-valued mappings in metric and Banach spaces. (English) Zbl 1120.47043 J. Nonlinear Convex Anal. 8, No. 1, 35-45 (2007). Some recent homotopy results given by B.Sims, H.K.Xu and G.X.Z.Yuan [in: Proceedings of the 6th international conference on nonlinear functional analysis and applications (Masan, Korea, September 1–5, 2000), 93–104 (2001; Zbl 1073.47519)] are here extended for set-valued mappings in the CAT(0) setting. Also, using an ultrapower approach, several fixed point theorems for nonexpansive mappings in Banach spaces are given. Reviewer: Adrian Petruşel (Cluj-Napoca) Cited in 142 Documents MSC: 47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc. 47H04 Set-valued operators 47H10 Fixed-point theorems 54H25 Fixed-point and coincidence theorems (topological aspects) 54C60 Set-valued maps in general topology Keywords:fixed point; nonexpansive mapping; Banach space Citations:Zbl 1073.47519 PDFBibTeX XMLCite \textit{S. Dhompongsa} et al., J. Nonlinear Convex Anal. 8, No. 1, 35--45 (2007; Zbl 1120.47043)