Turnpike theorem for a class of discrete time optimal control problems

In this paper we consider a discrete time optimal control problem determined by a continuous function v : K x K --> R-1, where K is a compact metric space. We study the structure of "approximate" solutions and show that each "approximate" optimal solution {x(i)}(i=0)(n) subset of K is a contained in a small neighborhood of y(v) is an element of K for all i is an element of {N, (...) , n - N}, where y(v) depends on v and N is a constant which depends on the neighborhood and does not depend on n.