\(\mathcal{I}_2\)-statistically and \(\mathcal{I}_2\)-lacunary statistically convergent double set sequences of order \(\eta\). (English) Zbl 1528.40006
Summary: In this study, for double set sequences, as a new approach to the notion of statistical convergence of order \(\eta \), the notions of Wijsman \(\mathcal{I}_2\) statistically convergence of order \(\eta \), Wijsman strong \(\mathcal{I}_2\)-Cesàro summability of order \(\eta \), Wijsman \(\mathcal{I}_2\)-lacunary statistically convergence of order \(\eta\) and Wijsman strong \(\mathcal{I}_2\)-lacunary summability of order \(\eta\) are introduced, where \(0< \eta \leq 1\). Also, some properties of these notions are investigated, some investigations about these are made and the existence of some relationships between them are examined.
MSC:
| 40A35 | Ideal and statistical convergence |
Keywords:
order \(\eta\); sequences of sets; Wijsman convergence; double sequence; \(\mathcal{I}\)-convergence; statistical convergence; lacunary sequenceReferences:
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