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Statistical convergence of double sequences in intuitionistic fuzzy normed spaces

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  • Mursaleen, M.
  • Mohiuddine, S.A.

Abstract

Recently, the concept of intuitionistic fuzzy normed spaces was introduced by Saadati and Park [Saadati R, Park JH. Chaos, Solitons & Fractals 2006;27:331–44]. Karakus et al. [Karakus S, Demirci K, Duman O. Chaos, Solitons & Fractals 2008;35:763–69] have quite recently studied the notion of statistical convergence for single sequences in intuitionistic fuzzy normed spaces. In this paper, we study the concept of statistically convergent and statistically Cauchy double sequences in intuitionistic fuzzy normed spaces. Furthermore, we construct an example of a double sequence to show that in IFNS statistical convergence does not imply convergence and our method of convergence even for double sequences is stronger than the usual convergence in intuitionistic fuzzy normed space.

Suggested Citation

  • Mursaleen, M. & Mohiuddine, S.A., 2009. "Statistical convergence of double sequences in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 41(5), pages 2414-2421.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:5:p:2414-2421
    DOI: 10.1016/j.chaos.2008.09.018
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    References listed on IDEAS

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    1. Alimohammady, M. & Roohi, M., 2006. "Compactness in fuzzy minimal spaces," Chaos, Solitons & Fractals, Elsevier, vol. 28(4), pages 906-912.
    2. Karakus, S. & Demirci, K. & Duman, O., 2008. "Statistical convergence on intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 35(4), pages 763-769.
    3. S. Karakus & K. Demırcı, 2007. "Statistical Convergence of Double Sequences on Probabilistic Normed Spaces," International Journal of Mathematics and Mathematical Sciences, Hindawi, vol. 2007, pages 1-11, June.
    4. Alaca, Cihangir & Turkoglu, Duran & Yildiz, Cemil, 2006. "Fixed points in intuitionistic fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 29(5), pages 1073-1078.
    5. Saadati, Reza & Park, Jin Han, 2006. "On the intuitionistic fuzzy topological spaces," Chaos, Solitons & Fractals, Elsevier, vol. 27(2), pages 331-344.
    6. Saadati, Reza, 2009. "A note on “Some results on the IF-normed spaces”," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 206-213.
    7. Saadati, Reza & Razani, Abdolrahman & Adibi, H., 2007. "A common fixed point theorem in L-fuzzy metric spaces," Chaos, Solitons & Fractals, Elsevier, vol. 33(2), pages 358-363.
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    Cited by:

    1. Mursaleen, M. & Mohiuddine, S.A., 2009. "Nonlinear operators between intuitionistic fuzzy normed spaces and Fréchet derivative," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1010-1015.
    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. Mohiuddine, S.A., 2009. "Stability of Jensen functional equation in intuitionistic fuzzy normed space," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2989-2996.
    4. Mursaleen, M. & Mohiuddine, S.A., 2009. "On stability of a cubic functional equation in intuitionistic fuzzy normed spaces," Chaos, Solitons & Fractals, Elsevier, vol. 42(5), pages 2997-3005.

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