Banach’s fixed point theorem for partial metric spaces. (English) Zbl 1080.54030

Summary: In 1994, S. G. Matthews introduced the notion of a partial metric space and obtained, among other results, a Banach contraction mapping for these spaces. Later on, S. J. O’Neill generalized Matthews’ notion of partial metric, in order to establish connections between these structures and the topological aspects of domain theory. Here, we obtain a Banach fixed point theorem for complete partial metric spaces in the sense of O’Neill. Thus, Matthews’ fixed point theorem follows as a special case of our result.


54H25 Fixed-point and coincidence theorems (topological aspects)
54E50 Complete metric spaces
54E99 Topological spaces with richer structures
68Q55 Semantics in the theory of computing