Serpil Pehlivan

Statistical cluster points and turnpike

In this paper we study an asymptotic behaviour of optimal paths of a difference inclusion. The turnpike property in some wording [5,8, and so on] provided that there is a certain stationary point and optimal paths converge to that point. In this case only a finite number terms of the path (sequence) remain on the outside of every neighbourhood of that point In the present paper a statistical cluster point introduced in [1] instead of the usual concept of limit point is considered and tue turnpiKe tueorem is proved, Mere it is es-ablished that there exists a stationary point which is a statistical cluster point for the all optimal paths. In this case not only a finite number but also infinite number terms of the path may remain on the outside of every small neighbourhood of the stationary point, but the number of these terms in comparison with the number of terms in the neighbourhood is so small that we can say:the path “almost” remains in this neighbourhood Note that the main results are obtained under certain assumptions which are essentially weaker than the usual convexity assumption. These assumptions first were introduced for continuous systems in [6]

Statistical limit inferior and limit superior for sequences of fuzzy numbers

In this paper, we extend the concepts of statistical limit superior and limit inferior (as introduced by Fridy and Orhan [Statistical limit superior and limit inferior, Proc. Amer. Math. Soc. 125 (12) (1997) 3625-3631. [12]]) to statistically bounded sequences of fuzzy numbers and give some fuzzy-analogues of properties of statistical limit superior and limit inferior for sequences of real numbers.

Statistically monotonic and statistically bounded sequences of fuzzy numbers

We introduce the statistical monotonicity and boundedness of a sequence of fuzzy numbers. We also derive the analogue of monotone convergence theorem and prove the decomposition theorems for this type of sequences.

Statistical Cluster Points of Sequences in Finite Dimensional Spaces

AbstractIn this paper we study the set of statistical cluster points of sequences in m-dimensional spaces. We show that some properties of the set of statistical cluster points of the real number sequences remain in force for the sequences in m-dimensional spaces too. We also define a notion of Γ-statistical convergence. A sequence xis Γ-statistically convergent to a set Cif Cis a minimal closed set such that for every ∈ > 0 the set

Strong Statistical Convergence in Probabilistic Metric Spaces

\{ k:\varrho (C,x_{{\text{ }}k} ) \geqslant \varepsilon \}

On weak ideal convergence in normed spaces

has density zero. It is shown that every statistically bounded sequence is Γ-statistically convergent. Moreover if a sequence is Γ-statistically convergent then the limit set is a set of statistical cluster points.

The core of a sequence of fuzzy numbers

In this paper, we investigate the relations between statistical limit superior (or statistical limit inferior) and statistical cluster points of a statistically bounded sequence of fuzzy numbers and show that the set of statistical cluster points of a sequence of this type might be empty.

Statistical continuity in probabilistic normed spaces

Abstract In this article, we introduce the concepts of strongly statistically convergent sequence and strong statistically Cauchy sequence in a probabilistic metric (PM) space endowed with the strong topology, and establish some basic facts. Next, we define the strong statistical limit points and the strong statistical cluster points of a sequence in this space and investigate the relations between these concepts.