Matthews introduced the idea of a partial metric area and obtained, among other results, Banak's contractive map of these distances. Later, S.J. O'Neill generalized Matthews' idea of partial scales, to establish links between these structures and topological aspects of field theory. Here, we get Banach's theory of the fixed point of full partial metric spaces in the sense of O'Neill. Therefore, Matthews fixed point theory remains a special case of our results. Keywords: Dualistic partial metric, partial metric, complete, quasi-metric, fixed point