Fixed Point Theory in Partial Metric Spaces

In 1992 Matthews [11] introduced the notion of a partial metric space as a part of the study of denotational semantics of dataflow networks. The main difference comparing to the standard metric is that the self-distance of an arbitrary point need not be equal to zero. This notion was originally motivated by the experience of computer science. The authors showed how a mathematics of nonzero self-distance for metric spaces has been established, and leads to interesting research into the foundations of topology [5], [9]. Many authors studied partial metric spaces and their topological properties, as well as fixed point resultsWe begin with the definition of a partial metric space by Matthews [11] as follows: