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Asymptotically lacunary statistical equivalence of double sequences of sets

Nuray F, Patterson R. F., Dündar E.

Demonstratio Mathematica

2016

Vol. 49, nr 2

183--196

The concepts of Wijsman asymptotically equivalence, Wijsman asymptotically statistically equivalence, Wijsman asymptotically lacunary equivalence and Wijsman asymptotically lacunary statistical equivalence for sequences of sets were studied by Ulusu and Nuray [24]. In this paper, we get analogous results for double sequences of sets.

Statistical convergence of sequences of sets

Nuray F, Rhoades B. E.

Fasciculi Mathematici

2012

Nr 49

87--99

The concept of convergence of sequences of points has been extended by several authors to convergence of sequences of sets. The three such extensions that we will consider in this paper are those of Kuratowski, Wijsman and Hausdorff. We shall define statistical convergence for sequences of sets and establish some basic theorems, thereby obtaining generalizations of the corre-sponding results for statistical convergence of sequences of points.