\(\lambda\)-\(\Delta^m\)-Statistical Convergence on Intuitionistic Fuzzy Normed Spaces





λ-statistical convergence, Difference sequences, Intuitionistic fuzzy normed space


The basic purpose of our work is to define $\lambda$-statistical convergence for the generalized difference sequences (i.e. \(\lambda\)-\(\Delta^m\)-statistical convergence) on Intuitionistic Fuzzy Normed space (IFN space). We have proven topological results about this generalized method of sequence convergence. Also, we have given the \(\lambda\)-\(\Delta^m\)-statistical Cauchy sequences along with its Cauchy criteria of convergence on these spaces.


Download data is not yet available.


A. Alotaibi and M. Mursaleen, Generalized statistical convergence of difference sequences, Advances in Difference Equations 2013 (2013), Article number: 212, DOI: 10.1186/1687-1847-2013-212.

R. Antal, M. Chawla and V. Kumar, Statistical Λ-convergence in intuitionistic fuzzy normed spaces, Buletinul Academiei de ¸ Stiin¸te a Republicii Moldova. Matematica 91(3) (2019), 22 – 33, URL: http://www.math.md/en/publications/basm/issues/y2019-n3/13130/.

R. Antal, M. Chawla, V. Kumar, and B. Hazarika. On Δm-statistical convergence double sequences in intuitionistic fuzzy normed spaces, Proyecciones 41(3) (2022), 697 – 713, DOI: 10.22199/issn.0717-6279-4633.

P. Baliarsingh, U. Kadak and M. Mursaleen, On statistical convergence of difference sequences of fractional order and related Korovkin type approximation theorems, Quaestiones Mathematicae 41(8) (2018), 1117 – 1133, DOI: 10.2989/16073606.2017.1420705.

R. Çolak, H. Altınok and M. Et, Generalized difference sequences of fuzzy numbers, Chaos, Solitons & Fractals 40(3) (2009), 1106 – 1117, DOI: 10.1016/j.chaos.2007.08.065.

M. Et and R. Çolak, On some generalized difference sequence spaces, Soochow Journal of Mathematics 21(4) (1995), 377 – 386.

M. Et and F. Nuray, Δm-statistical convergence, Indian Journal of Pure & Applied Mathematics 32(6) (2001), 961 – 969.

M. Et and H. ¸ Sengül, On (Δm, I)-lacunary statistical convergence of order α, Journal of Mathematical Analysis 7(5) (2016), 78 – 84, URL: http://www.ilirias.com/jma/repository/docs/JMA7-5-8.pdf.

H. Fast, Sur la convergence statistique, Colloquium Mathematicae 2(3-4) (1951), 241 – 244, URL: http://eudml.org/doc/209960.

A. L. Fradkov and R. J. Evans, Control of chaos: Methods and applications in engineering, Annual Reviews in Control 29(1) (2005), 33 – 56, DOI: 10.1016/j.arcontrol.2005.01.001.

R. Giles, A computer program for fuzzy reasoning, Fuzzy Sets and Systems 4(3) (1980), 221 – 234, DOI: 10.1016/0165-0114(80)90012-3.

B. Hazarika, Lacunary generalized difference statistical convergence in random 2-normed spaces, Proyecciones 31(4) (2012), 373 – 390, DOI: 10.4067/S0716-09172012000400006.

S. Karakus, K. Demirci and O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos, Solitons & Fractals 35(4) (2008), 763 – 769, DOI: 10.1016/j.chaos.2006.05.046.

H. Kizmaz, On certain sequence spaces, Canadian Mathematical Bulletin 24(2) (1981), 169 – 176, DOI: 10.4153/CMB-1981-027-5.

S. A. Mohiuddine and B. Hazarika, Some classes of ideal convergent sequences and generalized difference matrix operator, Filomat 31(6) (2017), 1827–1834, DOI: 10.2298/FIL1706827M.

S. A. Mohiunddine and Q. M. D. Lohani, On generalized statistical convergence in intuitionistic fuzzy normed space, Chaos, Solitons & Fractals 42(3) (2009), 1731 – 1737, DOI: 10.1016/j.chaos.2009.03.086.

M. Mursaleen, λ-statistical convergence, Mathematica Slovaca 50(1) (2000), 111 – 115, URL: http://dml.cz/handle/10338.dmlcz/136769.

J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals 22(5) (2004), 1039 – 1046, DOI: 10.1016/j.chaos.2004.02.051.

R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons & Fractals 27(2) (2006), 331 – 344, DOI: 10.1016/j.chaos.2005.03.019.

M. Sen and M. Et, Lacunary statistical and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed linear spaces, Boletim da Sociedade Paranaense de Matemática 38(1) (2020), 117 – 129, DOI: 10.5269/bspm.v38i1.34814.

B. C. Tripathy and A. Baruah, Lacunary statically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers, Kyungpook Mathematical Journal 50(4) (2010), 565 – 574, URL: https://kmj.knu.ac.kr/journal/view.html?spage=565&volume=50&number=4.

L. A. Zadeh, Fuzzy sets, Information and Control 8(3) (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.




How to Cite

Antal, R., & Chawla, M. (2024). \(\lambda\)-\(\Delta^m\)-Statistical Convergence on Intuitionistic Fuzzy Normed Spaces. Communications in Mathematics and Applications, 14(5), 1515–1527. https://doi.org/10.26713/cma.v14i5.2097



Research Article