A New Type of Difference I-Convergent Sequence in IFnNS

Authors

  • Vakeel A. Khan Department of Mathematics, Aligarh Muslim University, Aligarh, India
  • Izhar Ali Khan Department of Mathematics, Aligarh Muslim University, Aligarh, India
  • Mobeen Ahmad Department of Mathematics, Aligarh Muslim University, Aligarh, India

DOI:

https://doi.org/10.2298/YJOR210318022K

Keywords:

Difference sequences, I-Convergence, I-Cauchy, I*-Convergence, Intuitionistic fuzzy n-norm space

Abstract

In this paper, we introduce the notion of a generalized difference I-convergent (i.e.Δm-I-convergent) and difference I-Cauchy (i.e.Δm-I-Cauchy) sequence in intuitionistic fuzzy n-normed spaces. Further, we prove some results related to this notion. Also, we study the concepts of a generalized difference I*-convergent (i.e.Δm-I*-convergent) sequence in intuitionistic fuzzy n-normed spaces and show the relation between them.

References

L. A. Zadeh, “Fuzzy sets”, Information and Control, vol. 8, no. 3, pp. 338-353, 1965.

S. Gähler, “Lineare 2-normietre Räume”, Mathematische Nachrichten, vol. 28, no. 1-2, pp. 1-43, 1964.

S. Gähler, “Untersuchungen ¨uber verallgemeinerte m-metrische Räume”, Mathematische Nachrichten, vol. 40, no. 1-3, pp. 165-189, 1969.

S. S. Kim, and Y. J. Cho, “Strict convexity in linear n-normed spaces”, Demonstratio Mathematica, vol. 29, no. 4, pp. 739-744, 1996.

R. Malceski, “Strong n-convex n-normed spaces”, Matematički bilten, vol. 21, (1997), 81- 102.

H. Gunawan, and M. Mashadi, “On n -normed spaces”, International Journal of Mathematics and Mathematical Sciences, vol. 27, no. 10, pp. 631-639, 2001.

A. Narayanan, and S. Vijayabalaji, “Fuzzy n-normed linear space”, International Journal of Mathematics and Mathematical Sciences, vol. 24, pp. 3963-3977, 2005.

K. T. Atanassov, “Intuitionistic fuzzy sets”, Fuzzy sets and systems, vol. 20, no. 1, pp. 87-96, 1986.

G. Deschrijver, and E. Kerre, “On the cartesian product of intuitionistic fuzzy sets”, The journal of fuzzy mathematics, vol. 11, no 3, pp. 537-547, 2003.

D. Çoker, “An introduction to intuitionistic fuzzy topological spaces”, Fuzzy Sets and Systems, vol. 88, no. 1, pp. 81-89, 1997.

R. Saadati, and J. H. Park, “On the Intuitionistic fuzzy topological spaces sets”, Chaos Solitons and Fractal, vol. 22, pp. 331-344, 2006.

R. Saadati, and J. H. Park, “Intuitionistic Fuzzy Euclidian Normed Spaces”, Communications Mathematical Analysis, vol. 1, no. 2, pp. 85-90, 2006.

S. Vijayabalaji, N. Thillaigovindan, and Y. B. Jun, “Intuitionistic fuzzy n-normed linear space”, Bulletin of the Korean Mathematical Society, vol. 44, no. 2, pp. 291-308, 2007.

H. Fast, “Sur la convergence statistique”, Colloquium mathematicae, vol. 20, pp. 241-244, 1951.

P. Kostyrko, T. Ŝalát, and W. Wilczyński, “I-convergence”, Real Analysis Exchange, vol. 26, no. 2, pp. 669-686, 2000-2001.

B. C. Tripathy, M. Sen, and S. Nath, “On Generalized Difference Ideal Convergence in Generalized Probabilistic n-normed Spaces”, Proceedings of the National Academy of Sciences, India Section A: Physical Sciences, vol. 91, pp. 29-34, 2021.

M. Mursaleen, S. A. Mohiuddine, and H. H. Osama, “On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces”, Computers & mathematics with applications, vol. 59, no. 2, pp. 603-611, 2010.

V. A. Khan, M. Ahmad, H. Fatima, and M. F. Khan, “On some results in intuitionistic fuzzy ideal convergence double sequence spaces”, Advances in Difference Equations, vol. 2019, 375, 2019.

E. Sava，s, and M. Gürdal, “Certain summability methods in intuitionistic fuzzy normed spaces”, Journal of Intelligent & Fuzzy Systems, vol. 27, no. 4, pp. 1621-1629, 2014.

M. Sen, and P. Debnath, “Statistical convergence in intuitionistic fuzzy n-normed linear spaces”, Fuzzy Information and Engineering, vol. 3, no. 3, 259-273, 2011.

A. Esi, and B. Hazarika, “λ-ideal Convergence in Intuitionistic Fuzzy 2-normed Linear Space”, Journal of Intelligent and Fuzzy Systems, vol. 24, no. 4, pp. 725-732, 2013.

B. Hazarika, V. Kumar, and B. Lafuerza-Guillén, “Generalized ideal convergence in intuitionistic fuzzy normed linear spaces”, Filomat, vol. 27, no. 5, pp. 811-820, 2013.

B. Hazarika, “On σ-uniform Density and Ideal Convergent Sequences of Fuzzy Real Numbers”, Journal of Intelligent and Fuzzy Systems, vol. 26, no. 2, pp. 793-799, 2014.

B. Hazarika, “On σ-bounded Variation and Ideal Convergence of Fuzzy Sequences”, Journal of Intelligent and Fuzzy Systems, vol. 28, no. 1, pp. 411-420, 2015.

H. Kizmaz, “On certain sequence spaces”,Canadian Mathematical Bulletin, vol. 24, no. 2, pp. 169-176, 1981.

M. Et, and R. Çolak, “On generalized difference sequence spaces”, Soochow journal of mathematics, vol. 21, no. 4, pp. 377-386, 1995.

B. C. Tripathy, and A. Esi, “A new type of difference sequence spaces”, International Journal of Science & Technology, vol. 1, pp. 11-14, 2006.

H. G. Gumus, and F. Nuray, “Δm-ideal convergence”, Selcuk Journal of Applied Mathematics, vol. 12, no. 2, pp. 101-110, 2011.

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Published

2021-09-23

Issue

Vol. 33 No. 1 (2023)

Section

Research Articles

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