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Statistical cluster points and turnpike theorem in nonconvex problems. (English) Zbl 1161.91452
Summary: We develop the method suggested by {\it S. Pehlivan} and {\it M. A. Mamedov} [Optimization 48, No. 1, 93--106 (2000; Zbl 0963.40002)], where it was proved that under some conditions optimal paths have the same unique stationary limit point-stationary cluster point. This notion was introduced by {\it J. A. Fridy} [Proc. Am. Math. Soc. 118, No. 4, 1187--1192 (1993; Zbl 0776.40001)] and it turns out to be a very useful and interesting tool in turnpike theory. The purpose of this paper is to avoid the convexity conditions. Here the turnpike theorem is proved under conditions that are quite different from those of Pehlivan and Mamedov and may be satisfied for the mappings with nonconvex images and for nonconcave functions in the definition of functionals.

MSC:
91B62Growth models in economics
40A05Convergence and divergence of series and sequences
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Full Text: DOI
References:
[1] Fridy, J. A.: Statistical limit points. Proc. amer. Math. soc. 118, 1187-1192 (1993) · Zbl 0776.40001
[2] Makarov, V. L.; Rubinov, A. M.; Levin, M. J.: Mathematical economic theory: pure and mixed types of economic mechanisms. (1995) · Zbl 0834.90001
[3] Mamedov, M. A.: Turnpike theorems in continuous systems with integral functionals. Dokl. akad. Nauk. 323, 830-833 (1992) · Zbl 0788.90009
[4] Mckenzie, L. W.: Turnpike theory. Econometrica 44, 841-865 (1976) · Zbl 0356.90006
[5] S. Pehlivan, and, M. A. Mamedov, Statistical Cluster Points and Turnpike, submitted. · Zbl 0963.40002