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Zbl 1183.46070
Mursaleen, M.; Mohiuddine, S.A.
On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space. (English)
[J] J. Comput. Appl. Math. 233, No. 2, 142-149 (2009). ISSN 0377-0427

From the abstract: {\it J. A. Fridy} and {\it C. Orhan} [Pac. J. Math. 160, No. 1, 43--51 (1993; Zbl 0794.60012)] introduced the idea of lacunary statistical convergence. Quite recently, the concept of statistical convergence of double sequences has been studied in intuitionistic fuzzy normed space by the authors [Chaos Solitons Fractals 41, No. 5, 2414--2421 (2009; doi:10.1016/j.chaos.2008.09.018)]. In this paper, we study lacunary statistical convergence in intuitionistic fuzzy normed spaces. We also introduce here a new concept, that is, statistical completeness, and show that IFNS is statistically complete but not complete.

MSC 2000:: *46S40 Fuzzy functional analysis

Keywords: $t$-norm; $t$-conorm; intuitionistic fuzzy normed spaces; statistical convergence; lacunary statistical convergence; lacunary statistical Cauchy; statistical completeness

Citations: Zbl 0794.60012

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