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Statistical convergence of double sequences in intuitionistic fuzzy normed spaces. (English) Zbl 1198.40007

Summary: Recently, the concept of intuitionistic fuzzy normed spaces was introduced by R. Saadati and J. H. Park [Chaos Solitons Fractals 27, No. 2, 331–344 (2006; Zbl 1083.54514)]. S. Karakus, K. Demirci and O. Duman [Chaos Solitons and Fractals 35, No. 4, 763–769 (2008; Zbl 1139.54006)] 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.

Editorial remark: There are doubts about a proper peer-reviewing procedure of this journal. The editor-in-chief has retired, but, according to a statement of the publisher, articles accepted under his guidance are published without additional control.


MSC:
40G15Summability methods using statistical convergence
46S40Fuzzy functional analysis