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Characterization on $\mathcal{I}$-lacunary statistical convergence over different sequence spaces
  • Ekrem Savas,
  • Mandobi Banerjee,
  • Manasi Mandal
Ekrem Savas
Usak University 1 Eylul Campus

Corresponding Author:[email protected]

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Mandobi Banerjee
Jadavpur University
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Manasi Mandal
Jadavpur University
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Abstract

In this article we elaborately study certain characteristics of the set of all $\mathcal{I}$-lacunary statistical convergence sequences over various sequence spaces. Earlier results of some authors were mainly concerned regarding the closeness property of the sets: set of all bounded statistically convergent sequences, set of all bounded statistically convergent sequences of order $\alpha,$ set of all bounded $\mathcal{I}$-convergent sequences over the space $\ell^\infty$ ($\ell^\infty$- endowed with the sup-norm). Our approach is to examine different behaviors of the set of all $\mathcal{I}$-lacunary statistical convergence sequences over different sequence spaces. Finally we are able to impose some condition(s) over sequence spaces that turn the set of all $\mathcal{I}$-lacunary statistical convergence sequences to be a closed set.