On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space

The concept of statistical convergence was introduced by Fast [H. Fast, Sur la convergence statisticlue, Colloq. Math. 2 (1951) 241-244] which was later on studied by many authors. In [J.A. Fridy, C. Orhan, Lacunary statistical convergence, Pacific J. Math. 160 (1993) 43-51], Fridy and Orhan 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 Mursaleen and Mohiuddine [M. Mursaleen, S.A. Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos Solitons Fractals (2008), doi: 10.1016/j.chaos.2008.09.018]. In this paper, we study lacunary statistical convergence in intuitionistic fuzzy normed space. We also introduce here a new concept, that is, statistical completeness and show that IFNS is statistically complete but not complete. (C) 2009 Elsevier B.V. All rights reserved.