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Zbl 1120.47043
Dhompongsa, S.; Kirk, W.A.; Panyanak, B.
Nonexpansive set-valued mappings in metric and Banach spaces. (English)
[J] J. Nonlinear Convex Anal. 8, No. 1, 35-45 (2007). ISSN 1345-4773; ISSN 1880-5221/e

Some recent homotopy results given by {\it B.\,Sims, H.\,K.\thinspace Xu} and {\it G.\,X.\,Z.\thinspace 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.
[Adrian Petruşel (Cluj-Napoca)]

MSC 2000:: *47H09 Mappings defined by "shrinking" properties
47H04 Set-valued operators
47H10 Fixed point theorems for nonlinear operators on topol.linear spaces
54H25 Fixed-point theorems in topological spaces
54C60 Set-valued maps

Keywords: fixed point; nonexpansive mapping; Banach space

Citations: Zbl 1073.47519

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