On ideal convergence of triple sequences in intuitionistic Fuzzy normed space defined by compact operator





Ideal, Filter, T-norm, T-conorm, Intuitionistic fuzzy normed spaces


The main purpose of this article is to introduce and study some new spaces of I-convergence of triple sequences in intuitionistic fuzzy normed space defined by compact operator i.e 3SI(μ,ν)(T ) and 3SI0(μ,ν)(T ) and examine some fundamental properties, fuzzy topology and verify inclusion relations lying under these spaces.

Author Biographies

Vakeel A. Khan, Aligarh Muslim University.

Department of Mathematics.

Mohd. Imran Idrisi, Aligarh Muslim University.

Department of Mathematics

Umme Tuba, Aligarh Muslim University.

Department of Mathematics


A. Esi, “On some triple almost lacunary sequence spaces defined by Orlicz functions”, Research and Reviews: Discrete Mathematical Structures, vol. 1, no. 2, pp. 16-25, 2014.

A. Esi and C. Necdet, “Almost convergence of triple sequences”, Global journal of mathematical analysis, vol. 2, no. 1, pp. 6-10, 2014.

A. Sahiner, M. Gurdal, and K. Duden, “Triple sequences and their statistical convergence”, Selçuk Journal of Applied Mathematics, vol. 8, no. 2, pp. 49-55, 2007.

A. Sahiner and B. C. Tripathy, “Some I-related properties of Triple sequences”, Selçuk Journal of Applied Mathematics, vol. 9, no. 2, pp. 9-18, 2008.

B. C. Das, “Some I-convergent triple sequence spaces defined by a sequence of modulus function”, Proyecciones (Antofagasta), vol. 36, no. 1, pp. 117-130, 2017.

B. C. Tripathy, “Statistically convergent double sequences”, Tamkang Journal of Mathematics, vol.34, no. 3, pp. 231-237, 2003.

B. C. Tripathy and S. Mahanta, “On I-acceleration convergence of sequences”, Journal of the Franklin Institute, vol. 347, no. 3, pp. 591-598, 2010.

B. C. Tripathy, B. Chandra Hazarika and B. Choudhary, “Lacunary I-convergent sequences”, Kyungpook Mathematical Journal, vol. 52, no. 4, pp. 473-482, 2012.

B. C. Tripathy and Mausami Sen, “On fuzzy I-convergent difference sequence spaces”, Journal of intelligent & fuzzy systems, vol. 25, no. 3, pp. 643-647, 2013.

E. Savaş and M. Mursaleen, “On statistical convergent double sequences of fuzzy numbers”, Information Sciences, vol. 162, no. 3-4, pp. 183-192, 2004.

H. Fast, “Surla convergence statistique”, Colloquium mathematicae, vol. 2, no. 3-4, pp. 241-244, 1951.

I. J. Schoenberg, “The intregrability of certain functions and related summability methods”, The American mathematical monthly, vol. 66, no. 5, pp. 361-375, 1959.

K. T. Atanassov, “Intuitionistic fuzzy sets", Fuzzy Sets and Systems, vol. 20, pp. 87-96, 1986.

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

M. Mursaleen and Q. M. D. Lohni, “Intuitionistic fuzzy 2-normed space and some related concepts”, Chaos, Solitons & Fractals, vol. 42, no. 1, pp. 224-234, 2009.

M. Mursaleen and O. H. H. Edely, “Statistical convergence of double sequences”, Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 223-231, 2003.

P. Das, P. Kostyrko, W. Wilczynski, and P. Malik, “I and I∗- convergence of double sequences”, Mathematica Slovaca, vol. 58, no. 5, pp. 605-620, 2008.

P. Kostyrko, T. Salat, and W. Wilczynski, “I-convergence”, Real analysis exchange, vol. 26, no. 2, pp. 669-686, 2000.

R. Giles, “A computer program for fuzzy reasoning”, Fuzzy sets and systems, vol. 4, no. 3, pp. 221-234, 1980.

R. Saddati and J. H. Park, “On the intuitionistic fuzzy topological spaces”, Chaos, Solitons & Fractals, vol. 27, no. 2, pp. 331-4, 2006.

T. Salat, B. C. Tripathy, and M. Ziman, “On some properties of I convergence”, Tatra Mountain Mathematical Publications, vol. 28, no. 2, pp. 274-286, 2004.

V. A. Khan, K. Ebadullah, and Yasmeen, “On Zweier I-convergent sequence spaces”, Proyecciones (Antofagasta), vol. 33, no. 3, pp. 259-276, 2014.

V. A. Khan and K. Ebadullah, “Intuitionistic fuzzy Zweier I-convergent sequence spaces”, Functional Analysis: Theory, methods and applications, vol. 1, pp. 1-7, 2015.

V. A. Khan and Yasmeen, “Intuitionistic Fuzzy Zweier I-convergent Double Sequence Spaces”, New Trends in Mathematical Sciences, vol. 4, no. 2, pp. 240-247, 2016.

V. A. Khan, Yasmeen, “Intuitionistic fuzzy Zweier I-convergent double sequence spaces defined by modulus function”, Cogent Mathematics & Statistics, vol. 3, no. 1, 2016.



How to Cite

V. A. Khan, M. . Imran Idrisi, and U. Tuba, “On ideal convergence of triple sequences in intuitionistic Fuzzy normed space defined by compact operator”, Proyecciones (Antofagasta, On line), vol. 40, no. 5, pp. 1227-1247, Sep. 2021.