Honam Mathematical Journal (호남수학학술지)

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WIJSMAN LACUNARY IDEAL INVARIANT CONVERGENCE OF DOUBLE SEQUENCES OF SETS

  • Received : 2019.09.02
  • Accepted : 2020.01.28
  • Published : 2020.06.25
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Abstract

In this paper, we study the concepts of Wijsman lacunary invariant convergence, Wijsman lacunary invariant statistical convergence, Wijsman lacunary ${\mathcal{I}}_2$-invariant convergence (${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$), Wijsman lacunary ${\mathcal{I}}^*_2$-invariant convergence (${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$), Wijsman p-strongly lacunary invariant convergence ([W2Nσθ]p) of double sequence of sets and investigate the relationships among Wijsman lacunary invariant convergence, [W2Nσθ]p, ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$ and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$. Also, we introduce the concepts of ${\mathcal{I}}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence and ${\mathcal{I}}^{\ast}^{{\sigma}{\theta}}_{W_2}$-Cauchy double sequence of sets.

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References

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