\(\lambda\)-\(\Delta^m\)-Statistical Convergence on Intuitionistic Fuzzy Normed Spaces
DOI:
https://doi.org/10.26713/cma.v14i5.2097Keywords:
λ-statistical convergence, Difference sequences, Intuitionistic fuzzy normed spaceAbstract
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.
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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.
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