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On the Ideal Convergence of Double Sequences in Locally Solid Riesz Spaces

Author

Listed:
  • A. Alotaibi
  • B. Hazarika
  • S. A. Mohiuddine

Abstract

The aim of this paper is to define the notions of ideal convergence, I‐bounded for double sequences in setting of locally solid Riesz spaces and study some results related to these notions. We also define the notion of I*‐convergence for double sequences in locally solid Riesz spaces and establish its relationship with ideal convergence.

Suggested Citation

  • A. Alotaibi & B. Hazarika & S. A. Mohiuddine, 2014. "On the Ideal Convergence of Double Sequences in Locally Solid Riesz Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    • Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:396254
    DOI: 10.1155/2014/396254
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    References listed on IDEAS

    as
    1. S. A. Mohiuddine & Abdullah Alotaibi, 2013. "Statistical Summability of Double Sequences through de la Vallée‐Poussin Mean in Probabilistic Normed Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
    2. S. A. Mohiuddine & Abdullah Alotaibi & M. Mursaleen, 2012. "Statistical Convergence of Double Sequences in Locally Solid Riesz Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2012(1).
    3. S. A. Mohiuddine & Bipan Hazarika & Abdullah Alotaibi, 2013. "Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-8, July.
    4. S. A. Mohiuddine & Abdullah Alotaibi, 2013. "Statistical Summability of Double Sequences through de la Vallée-Poussin Mean in Probabilistic Normed Spaces," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-5, November.
    5. S. A. Mohiuddine & Abdullah Alotaibi & M. Mursaleen, 2012. "Statistical Convergence of Double Sequences in Locally Solid Riesz Spaces," Abstract and Applied Analysis, Hindawi, vol. 2012, pages 1-9, September.
    6. S. A. Mohiuddine & Bipan Hazarika & Abdullah Alotaibi, 2013. "Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2013(1).
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