zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces. (English) Zbl 1189.40003
Summary: Recently, the concept of statistical convergence of double sequences has been studied in intuitionistic fuzzy normed spaces by the first two authors [Chaos Solitons Fractals 41 2414--2421 (2009; Zbl 1198.40007)]. We know that ideal convergence is more general than statistical convergence for single or double sequences. This has motivated us to study the ideal convergence of double sequences in a more general setting. That is, in this paper, we study the concept of ideal convergence and ideal Cauchy for double sequences in intuitionistic fuzzy normed spaces.

40B05Multiple sequences and series
40A05Convergence and divergence of series and sequences
Full Text: DOI
[1] Zadeh, L. A.: Fuzzy sets, Inform. control 8, 338-353 (1965) · Zbl 0139.24606 · doi:10.1016/S0019-9958(65)90241-X
[2] Barros, L. C.; Bassanezi, R. C.; Tonelli, P. A.: Fuzzy modelling in population dynamics, Ecol. model. 128, 27-33 (2000)
[3] Fradkov, A. L.; Evans, R. J.: Control of chaos: methods and applications in engineering, Chaos solitons fractals 29, 33-56 (2005)
[4] Giles, R.: A computer program for fuzzy reasoning, Fuzzy sets and systems 4, 221-234 (1980) · Zbl 0445.03007 · doi:10.1016/0165-0114(80)90012-3
[5] Hong, L.; Sun, J. Q.: Bifurcations of fuzzy nonlinear dynamical systems, Commun. nonlinear sci. Numer. simul. 1, 1-12 (2006) · Zbl 1078.37049 · doi:10.1016/j.cnsns.2004.11.001
[6] Saadati, R.; Park, J. H.: On the intuitionistic fuzzy topological spaces, Chaos solitons fractals 27, 331-344 (2006) · Zbl 1083.54514 · doi:10.1016/j.chaos.2005.03.019
[7] Mursaleen, M.; Lohani, Q. M. D.: Intuitionistic fuzzy 2-normed space and some related concepts, Chaos, solitons fractals 42, 224-234 (2009) · Zbl 1200.46011 · doi:10.1016/j.chaos.2008.11.006
[8] Fast, H.: Sur la convergence statistique, Colloq. math. 2, 241-244 (1951) · Zbl 0044.33605
[9] Kastyrko, S.; Šalát, T.; Wilczyński, W.: I-convergence, Real anal. Exchange 26, 669-686 (2000)
[10] Nabiev, A.; Pehlivan, S.; Gurdal, M.: On I-Cauchy sequence, Taiwanese J. Math. 11, No. 2, 569-576 (2007) · Zbl 1129.40001
[11] Mursaleen, M.; Edely, Osama H. H.: Statistical convergence of double sequences, J. math. Anal. appl. 288, 223-231 (2003) · Zbl 1032.40001 · doi:10.1016/j.jmaa.2003.08.004
[12] Savaş, E.; Mursaleen, M.: On statistically convergent double sequences of fuzzy numbers, Inform. sci. 162, 183-192 (2004) · Zbl 1057.40002 · doi:10.1016/j.ins.2003.09.005
[13] Das, P.; Kastyrko, P.; Wilczyński, W.; Malik, P.: I and I$\ast $-convergence of double sequences, Math. slovaca 58, 605-620 (2008) · Zbl 1199.40026 · doi:10.2478/s12175-008-0096-x
[14] Mursaleen, M.; Mohiuddine, S. A.: Statistical convergence of double sequences in intuitionistic fuzzy normed spaces, Chaos, solitons fractals 41, 2414-2421 (2009) · Zbl 1198.40007 · doi:10.1016/j.chaos.2008.09.018