  In this paper we combine the notions of partial metric spaces with negative
distances, $G_p$-metric spaces and n-metric spaces together into one structure
called the partial n-metric spaces. These are generalizations of all the said
structures, and also generalize the notions of $G$-metric and $G_p$-metric
spaces to arbitrary finite dimension. We prove Cauchy mapping theorems and
other fixed point theorems for such spaces.
