Abstract
In the first part of the paper, following the works of Pehlivan et al. (2004), we study the set of all
A
-statistical cluster points of sequences in
m
-dimensional spaces and make certain investigations on the set of all
A
-statistical cluster points of sequences in
m
-dimensional spaces. In the second part of the paper, we apply this notion to study an asymptotic behaviour of optimal paths and optimal controls in the problem of optimal control in discrete time and prove a general version of turnpike theorem in line of the work of Mamedov and Pehlivan (2000). However, all results of this section are presented in terms of a more general notion of
ℐ
-cluster points.