Statistical Cluster Points and Turnpike Theorem in Nonconvex Problems

Abstract

In this paper we develop the method suggested by S. Pehlivan and M. A. Ž . Mamedov ''Statistical Cluster Points and Turnpike,'' submitted , 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 J. A. Fridy Ž . 1993, Proc. Amer. Math. Soc. 118, 1187᎐1192 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.

Statistical order convergence in Riesz spaces

“…Since then it has been studied by many authors. An important application of the theory can be found in [12]. The statistical convergence has also been discussed in more general abstract spaces such as locally convex spaces [11], Banach spaces [3,10], and fuzzy number spaces [14].…”

Statistical limit inferior and limit superior for sequences of fuzzy numbers

“…In the case of real sequences, Fridy [10] obtained the statistical analogue of Cauchy criterion of convergence. These concepts were used in Turnpike theory as an application [17,22]. Recently, Teran [27] showed a general method to translate Tauberian theorems for summability methods in R into Tauberian theorems for the corresponding forms of statistical convergence in metric spaces.…”

Deferred statistical cluster points of double sequences

“…Later on some generalizations and applications of these notions were investigated by many authors (see [5,7,8,12,14,19,23,24]). Some equivalence results for Cesàro submethods were studied by Goffman and Petersen [10], Armitage and Maddox [2] and Osikiewicz [17].…”