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\(A\)-statistical cluster points in finite dimensional spaces and application to turnpike theorem. (English) Zbl 07022211
Summary: In the first part of the paper, following the works of S. Pehlivan et al. [Czech. Math. J. 54, No. 1, 95–102 (2004; Zbl 1045.40004)], 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 M. A. Mamedov and S. Pehlivan [Math. Japon. 52, No. 1, 51–55 (2000; Zbl 0964.40001)]. However, all results of this section are presented in terms of a more general notion of \(\mathcal{I}\)-cluster points.

MSC:
49-XX Calculus of variations and optimal control; optimization
93-XX Systems theory; control
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