×

zbMATH — the first resource for mathematics

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.

MSC:
40B05 Multiple sequences and series (should also be assigned at least one other classification number in this section)
26E60 Means
40A05 Convergence and divergence of series and sequences
PDF BibTeX XML Cite
Full Text: DOI
References:
[1] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338-353, (1965) · Zbl 0139.24606
[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
[5] Hong, L.; Sun, J.Q., Bifurcations of fuzzy nonlinear dynamical systems, Commun. nonlinear sci. numer. simul., 1, 1-12, (2006) · Zbl 1078.37049
[6] Saadati, R.; Park, J.H., On the intuitionistic fuzzy topological spaces, Chaos solitons fractals, 27, 331-344, (2006) · Zbl 1083.54514
[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
[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), 2001
[10] Nabiev, A.; Pehlivan, S.; Gűrdal, M., On \(I\)-Cauchy sequence, Taiwanese J. math., 11, 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
[12] Savaş, E.; Mursaleen, M., On statistically convergent double sequences of fuzzy numbers, Inform. sci., 162, 183-192, (2004) · Zbl 1057.40002
[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
[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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.