Rough Ideal Statistical Convergence via Generalized Difference Operators in Intuitionistic Fuzzy Normed Spaces
DOI:
https://doi.org/10.26713/cma.v15i1.2423Keywords:
Ideal statistical convergence, Rough ideal statistical convergence, Intuitionistic fuzzy normed space, Difference SequenceAbstract
This study focuses on investigating the concept of rough ideal statistical convergence for generalized difference sequences in intuitionistic fuzzy normed spaces. We have studied the algebraic and topological properties of rough ideal statistical limit points for generalized difference sequence. Apart from this, we also investigated rough ideal statistical cluster points, the relation between rough I-statistical limit points and rough I-statistical cluster points for generalized difference sequence in intuitionistic fuzzy normed spaces.
Downloads
References
R. Antal, M. Chawla and V. Kumar, Rough statistical convergence in intuitionistic fuzzy normed spaces, Filomat 35(13) (2021), 4405 – 4416, DOI: 10.2298/FIL2113405A.
R. Antal, M. Chawla and V. Kumar, Rough statistical convergence in probabilistic normed spaces, Thai Journal of Mathematics 20(4) (2023), 1707 – 1719, URL: https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/1433.
M. Arslan and E. Dündar, On rough convergence in 2-normed spaces and some properties, Filomat 33(16) (2019), 5077 – 5086, DOI: 10.2298/FIL1916077A.
K. T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20(1) (1986), 87 – 96, DOI: 10.1016/S0165-0114(86)80034-3.
S. Aytar, Rough statistical convergence, Numerical Functional Analysis and Optimization 29(3-4) (2008), 291 – 303, DOI: 10.1080/01630560802001064.
M. Balcerzak, K. Dems and A. Komisarski, Statistical convergence and ideal convergence for sequences of functions, Journal of Mathematical Analysis and Applications 328(1) (2007), 715 – 729, DOI: 10.1016/j.jmaa.2006.05.040.
A. K. Banerjee and A. Banerjee, I-convergence classes of sequences and nets in topological spaces, Jordan Journal of Mathematics and Statistics 11(1) (2018), 13 – 31, URL: https://journals.yu.edu.jo/jjms/Issues/Vol11No12018PDF/2.pdf.
A. K. Banerjee and A. Banerjee, A study on I-Cauchy sequences and I-divergence in S-metric spaces, Malaya Journal of Matematik 6(2) (2018), 326 – 330, DOI: 10.26637/MJM0602/0004.
A. K. Banerjee and A. Paul, Rough I-convergence in cone metric spaces, Journal of Mathematical and Computational Science 12 (2022), Article ID 78, DOI: 10.28919/jmcs/6808.
P. Das, E. Savas and S. K. Ghosal, On generalizations of certain summability methods using ideals, Applied Mathematics Letters 24(9) (2011), 1509 – 1514, DOI: 10.1016/j.aml.2011.03.036.
S. Debnath and N. Subramanian, Rough statistical convergence on triple sequences, Proyecciones (Antofagasta) 36(4) (2017), 685 – 699, DOI: 10.4067/S0716-09172017000400685.
N. Demir and H. Gümü¸s, Rough convergence for difference sequences, New Trends in Mathematical Sciences 8(2) (2020), 22 – 28, DOI: 10.20852/ntmsci.2020.402.
N. Demir and H. Gümü¸s, Rough statistical convergence for difference sequences, Kragujevac Journal of Mathematics 46(5) (2022), 733 – 742, DOI: 10.46793/KgJMat2205.733D.
M. Et and R. Çolak, On some generalized difference sequence spaces, Soochow Journal of Mathematics 21(4) (1995), 377 – 386.
H. Fast, Sur la convergence staistique, Colloquium Mathematicae 2(3-4) (1951), 241 – 244, URL: http://eudml.org/doc/209960.
G. Karabacak and A. Or, Rough statistical convergence for generalized difference sequences, Electronic Journal of Mathematical Analysis and Applications, 11(1) (2023), 222 – 230, URL: https://ejmaa.journals.ekb.eg/article_285269_837f027ea0bd32dab4a5474ffb5a1991.pdf.
S. Karakus, K. Demirci and O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos Salitons & Fractals 35(4) (2008), 763 – 769, DOI: 10.1016/j.chaos.2006.05.046.
Ö. Ki¸si and E. Dündar, Rough I2-lacunary statistical convergence of double sequences, Journal of Inequalities and Applications 2018 (2018), Article number: 230, DOI: 10.1186/s13660-018-1831-7.
H. Kizmaz, On certain sequence spaces, Canadian Mathematical Bulletin 24(2) (1981), 169 – 176, DOI: 10.4153/CMB-1981-027-5.
P. Kostyrko, M. Máˇcaj, T. Šalát and M. Sleziak, I-convergence and extremal I-limit points, Mathematica Slovaca 55(4) (2005), 443 – 464, URL: http://dml.cz/dmlcz/132906.
P. Kostyrko, W. Wilczy ´ nski and T. Šalát, I-convergence, Real Analysis Exchange 26(2) (2000/2001), 669 – 685, URL: https://projecteuclid.org/journals/real-analysis-exchange/volume-26/issue-2/IConvergence/rae/1214571359.full?tab=ArticleLink.
F. Lael and K. Nourouzi, Some results on the IF-normed spaces, Chaos, Solitons & Fractals 37(2) (2008), 931 – 939, DOI: 1016/j.chaos.2006.10.019.
B. K. Lahiri and P. Das, Further results on I-limit superior and limit inferior, Mathematical Communications 8(2) (2003), 151 – 156, URL: https://hrcak.srce.hr/726.
P. Malik and M. Maity, On rough convergence of double sequence in normed linear spaces, Bulletin of the Allahabad Mathematical Society 28 (2013), 89 – 99, URL: https://www.amsallahabad.org/pdf/bams281.pdf.
P. Malik and M. Maity, On rough statistical convergence of double sequences in normed linear spaces, Afrika Matematika 27 (2016), 141 – 148, DOI: 10.1007/s13370-015-0332-9.
S. K. Pal, C. H. Debraj and S. Dutta, Rough ideal convergence, Hacettepe Journal of Mathematics and Statistics 42(6) (2013), 633 – 640, URL: https://dergipark.org.tr/en/pub/hujms/issue/7745/101241.
J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons & Fractals 22(5) (2004), 1039 – 1046, DOI: 10.1016/j.chaos.2004.02.051.
H. X. Phu, Rough convergence in normed linear spaces, Numerical Functional Analysis and Optimization 22(1-2) (2001), 199 – 222, DOI: 10.1081/NFA-100103794.
H. X. Phu, Rough convergence in infinite dimensional normed spaces, Numerical Functional Analysis and Optimization 24(3-4) (2003), 285 – 301, DOI: 10.1081/NFA-120022923.
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.
E. Sava¸s and M. Gürdal, Certain summability methods in intuitionistic fuzzy normed spaces, Journal of Intelligent & Fuzzy Systems 27(4) (2014), 1621 – 1629, DOI: 10.3233/IFS-141128.
I. J. Schoenberg, The integrability of certain functions and related summability methods II, The American Mathematical Monthly 66(7) (1959), 562 – 563, DOI: 10.1080/00029890.1959.11989350.
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.
H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloquium Mathematicum 2 (1951), 73 – 74.
L. A. Zadeh, Fuzzy sets, Information and Control 8(3) (1965), 338 – 353, DOI: 10.1016/S0019-9958(65)90241-X.
A. Zygmund, Trigonometric Series, 3rd edition, Volumes I & II combined, Cambridge University Press, Cambridge (1979).
Downloads
Published
How to Cite
Issue
Section
License
Authors who publish with this journal agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.