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In this paper we consider partial metric spaces in the sense of O'Neill. Weintroduce the notions of strong partial metric spaces and Cauchy functions. Weprove a fixed point theorem for such spaces and functions that improvesMatthews' contraction mapping theorem in two ways. First, the existence offixed points now holds for a wider class of functions and spaces. Second, ourtheorem also allows for fixed points with nonzero self-distances. We also provefixed point theorems for orbitally $r$-contractive and orbitally$\phi_r$-contractive maps. We then apply our results to give alternative proofsof some of the other known fixed point theorems in the context of partialmetric spaces.

Partial metric spaces with negative distances and fixed point theorems