Lacunary statistical convergence of double sequences of sets

Abstract

In this paper, we study the concepts of Wijsman statistical convergence, Wijsman lacunary statistical convergence, Wijsman lacunary convergence and Wijsman strongly lacunary convergence double sequences of sets and investigate the relationship among them.

Asymptotically Lacunary Statistical Equivalence of Double Sequences of Sets

“…Now, we recall the basic definitions and concepts (See [1,2,3,4,5,9,10,12,13,14,15,16,17,18,21,22,23,24,25,26]). …”

“…The concept of convergence of sequences of numbers has been extended by several authors to convergence of sequences of sets (see, [3,4,5,12,25,26]). Nuray and Rhoades [12] extended the notion of convergence of set sequences to statistical convergence and gave some basic theorems.…”

“…Nuray and Rhoades [12] extended the notion of convergence of set sequences to statistical convergence and gave some basic theorems. Ulusu and Nuray [23] defined the Wijsman lacunary statistical convergence of sequence of sets and considered its relation with Wiijsman statistical convergence, which was defined by Nuray and Rhoades.…”

“…al. [13] studied Wijsman statistical convergence, Hausdorff statistical convergence and Wijsman statistical Cauchy double sequences of sets and investigated the relationship between them.…”

Wijsman $\lambda-$statistical convergence of interval numbers

“…The concepts of Wijsman statistical convergence and boundedless for the sequence (A k ) were given by Nuray and Rhoades [17] as follows: Let (X, ρ) be a metric space. For any non-empty closed subsets A, A k ⊂ X (k ∈ N) , we say that the sequence (A k ) is Wijsman statistical convergent to A if the sequence (d(x, A k )) is statistically convergent to d(x, A), i.e., for ε > 0 and for each x ∈ X lim…”