Banach's fixed point theorem for partial metric spaces

Abstract

In 1994, S.G. Matthews introduced the notion of a par- tial metric space and obtained, among other results, a Banach contraction mapping for these spaces. Later on, S.J. O’Neill gen- eralized 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 special case of our result.