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Double Lacunary Density and Some Inclusion Results in Locally Solid Riesz Spaces

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  • S. A. Mohiuddine
  • Bipan Hazarika
  • Abdullah Alotaibi

Abstract

We define the notions of double statistically convergent and double lacunary statistically convergent sequences in locally solid Riesz space and establish some inclusion relations between them. We also prove an extension of a decomposition theorem in this setup. Further, we introduce the concepts of double θ‐summable and double statistically lacunary summable in locally solid Riesz space and establish a relationship between these notions.

Suggested Citation

  • 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).
    • Handle: RePEc:wly:jnlaaa:v:2013:y:2013:i:1:n:507962
    DOI: 10.1155/2013/507962
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    References listed on IDEAS

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    1. 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).
    2. Mohiuddine, S.A. & Danish Lohani, Q.M., 2009. "On generalized statistical convergence in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1731-1737.
    3. Jinlu Li, 2000. "Lacunary statistical convergence and inclusion properties between lacunary methods," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 23, pages 1-6, January.
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    1. 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).
    2. 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).

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