A Globally Stable Fixed Point in an Ordered Partial Metric Space

The research in this paper was motivated by Kamihigashi and Stachurski [11], and Matthews [14]. The application of the research made by Kamihigashi and Stachurski [11] does not cover some set of real life problems; as some problems are not compatible with normal metric (d) they used. In a move to cover such problems, a partial metric was used and an analogue operator of asymptotic contraction in a partial metric space was introduced, the existence of a globally stable fixed point in an ordered partial metric space was established. The results we obtained extend and improve the applicability of many existing results in the literature. In particular, the results we obtained covered the research of Kamihigashi and Stachurski [11] and can have a real life application in computer semantics as earlier shown by Matthews [14].