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Wijsman lacunary invariant statistical convergence for triple sequences via Orlicz function. (English) Zbl 1499.40011

Summary: In this paper, we generalized the Wijsman lacunary invariant statistical convergence of closed sets in metric space by introducing the Wijsman lacunary invariant statistical \(\tilde{\phi}\) convergence for the sets of triple sequences. We introduce the concepts of Wijsman invariant \(\tilde{\phi} \)-convergence, Wijsman invariant statistical \(\tilde{\phi} \)-convergence, Wijsman lacunary invariant \(\tilde{\phi}\)-convergence, Wijsman lacunary invariant statistical \(\tilde{\phi} \)-convergence for the sets of triple sequences. In addition, we investigate existence of some relations among these new notations for the sets of triple sequences.

MSC:

40A05 Convergence and divergence of series and sequences
40C05 Matrix methods for summability
40D25 Inclusion and equivalence theorems in summability theory
54B20 Hyperspaces in general topology
40B05 Multiple sequences and series
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