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On the difference spaces of almost convergent and strongly almost convergent double sequences

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In this paper, we study the difference spaces \({\mathcal {F}}(\varDelta )\), \({\mathcal {F}}_0(\varDelta )\), \({\mathcal {[F]}}(\varDelta )\) and \({\mathcal {[F]}}_0(\varDelta )\) of double sequences obtained as the domain of four-dimensional backward difference matrix \(\varDelta \) in the spaces \({\mathcal {F}}\), \({\mathcal {F}}_{0}\), \({\mathcal {[F]}}\) and \({\mathcal {[F]}}_{0}\) of almost convergent, almost null, strongly almost convergent and strongly almost null double sequences; respectively. We examine general topological properties of those spaces and give some inclusion theorems. Furthermore, we deal with their dual spaces.

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Author notes

  1. Feyzi Başar

    Present address: KısıklıMah. Alim Sok, Alim Apt. No: 7/6, 34692, Üsküdar, İstanbul, Turkey

Authors and Affiliations

  1. İstanbul University, Beyazıt Campus, 34134, İstanbul, Turkey

    Hüsamettin Çapan

  2. İnönü University, 44280, Malatya, Turkey

    Feyzi Başar

Authors
  1. Hüsamettin Çapan
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  2. Feyzi Başar
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Correspondence to Feyzi Başar.

Additional information

The main results of this paper were presented at International Conference of Mathematical Sciences (ICMS 2018) to be held 31 July–06 August 2018 at Maltepe University, İstanbul, Turkey.

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Çapan, H., Başar, F. On the difference spaces of almost convergent and strongly almost convergent double sequences. Positivity 23, 493–506 (2019). https://doi.org/10.1007/s11117-018-0620-3

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  • DOI: https://doi.org/10.1007/s11117-018-0620-3

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