Wijsman Lacunary \({\mathbf{\mathcal{I}}}\)-Invariant Convergence of Sequences of Sets

Abstract

In this paper, we study the concepts of Wijsman lacunary \({\mathcal{I}}\)-invariant convergence \(\left( {{\mathcal{I}}_{\sigma \theta }^{W} } \right),\) Wijsman lacunary \({\mathcal{I}}^{ *}\)-invariant convergence \(\left( {{\mathcal{I}}_{\sigma \theta }^{ *W} } \right),\) Wijsman \(p\)-strongly lacunary invariant convergence \(\left( {[WN_{\sigma \theta } ]_{p} } \right)\) of sequences of sets and investigate the relationships among Wijsman lacunary invariant convergence, \([WN_{\sigma \theta } ]_{p}\), \({\mathcal{I}}_{\sigma \theta }^{W}\) and \({\mathcal{I}}_{\sigma \theta }^{ *W}\). Also, we introduce the concepts of \({\mathcal{I}}_{\sigma \theta }^{W}\)-Cauchy sequence and \({\mathcal{I}}_{\sigma \theta }^{ *W}\)-Cauchy sequence of sets.

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Acknowledgements

This study is supported by Afyon Kocatepe University Scientific Research Coordination Unit with the project number 17.KARİYER.20 conducted by Erdinç Dündar.

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Correspondence to Erdinç Dündar.

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Dündar, E., Pancaroğlu Akın, N. & Ulusu, U. Wijsman Lacunary \({\mathbf{\mathcal{I}}}\)-Invariant Convergence of Sequences of Sets. Proc. Natl. Acad. Sci., India, Sect. A Phys. Sci. (2020). https://doi.org/10.1007/s40010-020-00694-w

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Keywords

  • Lacunary sequence
  • Invariant convergence
  • \({\mathcal{I}}\)-convergence
  • Wijsman convergence
  • Cauchy sequence
  • Sequences of sets

2010 Mathematics Subject Classification

  • 40A05
  • 40A35