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Zbl 1198.40007
Mursaleen, M.; Mohiuddine, S.A.
Statistical convergence of double sequences in intuitionistic fuzzy normed spaces. (English)
[J] Chaos Solitons Fractals 41, No. 5, 2414-2421 (2009). ISSN 0960-0779

Summary: Recently, the concept of intuitionistic fuzzy normed spaces was introduced by {\it R. Saadati} and {\it J. H. Park} [Chaos Solitons Fractals 27, No. 2, 331--344 (2006; Zbl 1083.54514)]. {\it S. Karakus, K. Demirci} and {\it 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. \par 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 2000:: *40G15
46S40 Fuzzy functional analysis

Citations: Zbl 1083.54514; Zbl 1139.54006

Cited in: Zbl 1228.40010 Zbl 1189.40003

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Zentralblatt MATH Berlin [Germany]