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A fixed point theorem and some properties of \(v\)-generalized metric spaces. (English) Zbl 1489.54027

Summary: We give a characterization of complete \(v\)-generalized metric spaces in terms of the fixed point property. Moreover, for such spaces, we prove Matkowski’s fixed point theorem. In the case of two-generalized metric spaces, we obtain a characterization of uniform continuity in terms of the distance function between two sets.

MSC:

54E50 Complete metric spaces
54C05 Continuous maps
54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
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