Bouamama, Sara; Misane, Driss Hyperconvex ultrametric spaces and fixed point theory. (English) Zbl 1091.54017 N. Z. J. Math. 34, No. 1, 25-29 (2005). Drawing inspiration from the known papers of R. C. Sine [Nonlinear Anal., Theory Methods Appl. 13, No. 7, 863–869 (1989; Zbl 0694.54033)] and P. Soardi [Proc. Am. Math. Soc. 73, 25–29 (1979; Zbl 0371.47048)], the authors introduce the notion of hyperconvexity in ultrametric spaces. Then they establish a fixed point theorem in such spaces for nonexpansive mappings and two related corollaries. Reviewer: Salvatore Sessa (Napoli) Cited in 1 ReviewCited in 2 Documents MSC: 54H25 Fixed-point and coincidence theorems (topological aspects) 47H10 Fixed-point theorems Keywords:ultrametric space; hyperconvexity; nonexpansive mapping Citations:Zbl 0694.54033; Zbl 0371.47048 PDFBibTeX XMLCite \textit{S. Bouamama} and \textit{D. Misane}, N. Z. J. Math. 34, No. 1, 25--29 (2005; Zbl 1091.54017)