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Hyperconvex ultrametric spaces and fixed point theory. (English) Zbl 1091.54017

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.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
47H10 Fixed-point theorems
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