A fixed point theorem in a generalized metric space. (English) Zbl 1137.54024

Das, Pratulananda; Dey, Lakshmi Kanta

Soochow J. Math. 33, No. 1, 33-39 (2007).

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.

Reviewer: In-Sook Kim (München)

MSC:

54H25

Fixed-point and coincidence theorems (topological aspects)

Keywords:

fixed point; generalized metric space

Citations:

Zbl 0096.17101