  Mustafa and Sims [12] introduced the notion of $G$-metric as a possible
generalization of usual notion of a metric space. The author generalized the
notion of G-metric to more than three variables and introduced the concept of
Generalized $n$-metric spaces [10]. In this paper, We prove Banach fixed point
theorem and a Suzuki-type fixed point theorem in Generalized $n$-metric spaces.
We also discuss applications to certain functional equations arising in dynamic
programming.
