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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.

Rough I-convergence

Dündar E., Çakan C.

Demonstratio Mathematica

2014

Vol. 47, nr 3

638--651

In this work, using the concept of I-convergence and using the concept of rough convergence, we introduced the notion of rough I-convergence and the set of rough I-limit points of a sequence and obtained two rough I-convergence criteria associated with this set. Later, we proved that this set is closed and convex. Finally, we examined the relations between the set of I-cluster points and the set of rough I-limit points of a sequence.