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A fixed point theorem in a generalized metric space. (English) Zbl 1137.54024
In this paper, a fixed point theorem of M. Edelstein [Proc. Am. Math. Soc. 12, 7–10 (1961; Zbl 0096.17101)] for uniformly locally contractive mappings is generalized. Instead of a complete metric space in the original theorem, the authors adopted a \(T\)-orbitally complete generalized metric space. Here a generalized metric space assumes a condition slightly more general than the triangle inequality.

MSC:
54H25 Fixed-point and coincidence theorems (topological aspects)
Citations:
Zbl 0096.17101
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