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Abstract and Applied Analysis
Volume 2014 (2014), Article ID 354846, 7 pages
http://dx.doi.org/10.1155/2014/354846
Research Article

A-Statistical Cluster Points in Finite Dimensional Spaces and Application to Turnpike Theorem

1Department of Mathematics, Jadavpur University, Kolkata West Bengal, 700032, India
2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 6 August 2013; Accepted 19 December 2013; Published 28 January 2014

Academic Editor: Andrew Pickering

Copyright © 2014 Pratulananda Das et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

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 -cluster points.