I-convergent triple fuzzy normed spaces

Authors

  • Tanweer Jalal National Institute of Technology Srinagar.
  • Ishfaq Ahmad Malik National Institute of Technology Srinagar.

DOI:

https://doi.org/10.22199/issn.0717-6279-4867

Keywords:

triple sequence, statistical convergence, fuzzy normed space, lacunary convergence, I-convergence

Abstract

In this paper we introduce the lacunary ideal convergence of triple sequences in fuzzy normed spaces and the relation between lacunary convergence and lacunary ideal convergence is investigated for triple sequences in fuzzy normed spaces. Concept of limit point and cluster point for triple sequences in fuzzy normed spaces and theorems related to these concepts are also given.

Author Biographies

Tanweer Jalal, National Institute of Technology Srinagar.

Department of Mathematics.

Ishfaq Ahmad Malik, National Institute of Technology Srinagar.

Department of Mathematics.

References

S. Debnath, B. Sarma and B. C. Das, “Statistically convergent triple sequence space defined by Orlicz functions”, Journal of Mathematical Analysis, vol. 4, no. 2, pp. 16-22, 2013. [On line]. Available: https://bit.ly/2VX5XAl

S. Debnath, B. Sarma and B. C. Das, “Some generalized triple sequence spaces of real numbers”, Journal of Nonlinear Analysis and Optimization: Theory & Applications, vol. 6, no. 1, pp. 71-79, 2015.

A. Esi, “On some triple almost lacunary sequence spaces defined by Orlicz functions”, Research and Reviews: Discrete Mathematical structures, vol. 1, pp. 16-25, 2014. [On line]. Available: https://bit.ly/2Mym1pj

A. Esi and M. N. Catalbas, “Almost convergence of triple sequences”, Global Journal of Mathematical Analysis, vol. 2, no. 1, pp. 6-10, 2014. https://doi.org/10.14419/gjma.v2i1.1709

A. Esi and E. Savas, “On lacunary statiscally convergent triple sequences in probabilistic normed space”, Applied Mathematics & Information Sciences. An International Journal, vol. 9, pp. 2529-2534, 2015. https://doi.org/10.12785/amis/090537

H. Fast, “Sur la convergence statistique”, Colloquium Mathematicum, vol. 2, pp. 241-244, 1951. https://doi.org/10.4064/cm-2-3-4-241-244

J. A. Fridy, “On statistical convergence”, Analysis: International mathematical journal of Analysis and its Applications, vol. 5, no. 4, pp. 301-313, 1985. https://doi.org/10.1524/anly.1985.5.4.301

J. A. Fridy, “Statistical limit points”, Proceedings of the American Mathematical Society, vol. 118, no. 4, pp. 1187-1192, 1993. https://doi.org/10.1090/s0002-9939-1993-1181163-6

B. Hazarika, “On ideal convergent sequences in fuzzy normed linear spaces”, Afrika Matematika, v.25, no. 4, pp. 987-999, 2013. https://doi.org/10.1007/s13370-013-0168-0

T. Jalal, “Some new I-convergent sequence spaces defined by using a sequence of modulus functions in n-normed spaces”, International Journal of Mathematical Archive, vol. 5, no. 9, pp. 202-209, 2014. [On line]. Available: https://bit.ly/3KaVP06

T. Jalal, Some new I-lacunary generalized difference sequence spaces defined in n-normed spaces, In: Vinai K. Singh (Ed.), Modern Mathematical Methods and High Performance Computing in Science and Technology, Springer Proceedings in Mathematics & Statistics, vol. 171, pp. 249-258, 2016. https://doi.org/10.1007/978-981-10-1454-3_21

T. Jalal and I. A. Malik, “I-convergence of triple difference sequence spaces over n-normed space”, Tbilisi Mathematical Journal, vol. 11, no. 4, pp. 93-102, 2018. https://doi.org/10.32513/tbilisi/1546570888

T. Jalal and I. A. Malik, “Some new triple sequence spaces over n-normed space”, Proyecciones (Antofagasta), vol. 37, no. 3, pp. 547-564, 2018. https://doi.org/10.4067/s0716-09172018000300547

P. Kostyrko, T. Salat, W. Wilczynski, “I-convergence”, Real Analysis Exchange, vol. 26, no. 2, pp. 669-686, 2000. https://doi.org/10.2307/44154069

V. Kumar, “On I-convergence of double sequences”, Mathematical Communications, vol. 12, no. 2, pp. 171-181, 2007.

M. Matloka, “Sequences of fuzzy numbers”, BUSEFAL, vol. 28, pp. 28-37, 1986.

M. Mursaleen and O. H. H. Edely, “Statistical convergence of doublé sequences”, Journal of Mathematical Analysis and Applications, vol. 288, no. 1, pp. 223-231, 2003.https://doi.org/10.1016/j.jmaa.2003.08.004

S. Nanda, “On sequences of fuzzy numbers”, Fuzzy Sets and Systems, vol. 33, no. 1, pp. 123-126, 1989. https://doi.org/10.1016/0165-0114(89)90222-4

R. Saadati, S.M. Vaezpour, Some results on fuzzy Banach spaces”, Journal of Applied Mathematics and Computing, vol. 17, pp. 475-484, 2005. https://doi.org/10.1007/BF02936069

T. Salat, B. C. Tripathy, M. Ziman, “On some properties of I-convergence”, Tatra Mountain Mathematical Publications, pp. 669-686, 2000.

A. Sahiner, M. Gurdal and F. K. Duden, “Triple Sequences and their statistical convergence”, Selcuk Journal of Applied Mathematics, vol. 8, pp. 49-55, 2007.

A. Sahiner and B.C. Tripathy, “Some I related properties of triple sequences”, Selcuk Journal of Applied Mathematics, vol. 9, pp. 9-18, 2008.

C. Sencimen and S. Pehlivan, “Statistical convergence in fuzzy normed linear spaces”, Fuzzy Sets and Systems, vol. 159, no. 3, pp. 361-370, 2008. https://doi.org/10.1016/j.fss.2007.06.008

B. C. Tripathy, “Statistically convergent double sequence”, Tamkang Journal of Mathematics, vol. 34, no. 3, pp. 231-237, 2003. https://doi.org/10.5556/j.tkjm.34.2003.314

B. C. Tripathy, and A. Baruah, “Lacunary statistically convergent and lacunary strongly convergent generalized difference sequences of fuzzy real numbers”, Kyungpook mathematical journal, vol. 50, no. 4, pp. 565-574, 2010. https://doi.org/10.5666/kmj.2010.50.4.565

B. C. Tripathy; B. Hazarika and B. Choudhary, “Lacunary I-convergent sequences”, Kyungpook mathematical journal, vol. 52 (4), 473-482, 2012. https://doi.org/10.5666/kmj.2012.52.4.473

B. C. Tripathy and A. J. Dutta, “Lacunary bounded variation sequence of fuzzy real numbers”, Journal of Intelligent & Fuzzy Systems, vol. 24, no. 1, 185-189, 2013. https://doi.org/10.3233/ifs-2012-0544

B. C. Tripathy and R. Goswami, “On triple difference sequences of real numbers in probabilistic normed spaces”, Proyecciones (Antofagasta), vol. 33, no. 2, pp. 157-174, 2014. https://doi.org/10.4067/s0716-09172014000200003

B. C. Tripathy and M. Sen, “On lacunary strongly almost convergent double sequences of fuzzy numbers”, Annals of the University of Craiova-Mathematics and Computer Science Series, vol. 42, no. 2, pp. 254-259, 2015.

B. C. Tripathy and A. J. Dutta, “Lacunary I-convergent sequences of fuzzy real numbers”, Proyecciones (Antofagasta), vol. 34, no. 3, pp. 205-218, 2015. https://doi.org/10.4067/s0716-09172015000300001

B. C. Tripathy and R. Goswami, “Statistically convergent multiple sequences in probabilistic normed spaces”, UPB Scientific Bulletin, Series A: Applied Mathematics and Physics, vol. 78, no. 4, pp. 83-94, 2016.

P. J. Dowari and B. C. Tripathy, “Lacunary convergence of double sequences of complex uncertain variables”, Journal of Uncertain Systems, vol. 14, no. 3, 2150017, 2021. https://doi.org/10.1142/S1752890921500173

B. C. Tripathy, R. Goswami, “On triple difference sequences of real numbers in probabilistic normed spaces”, Proyecciones (Antofagasta), vol. 33, no. 2, pp. 157-174, 2014. https://doi.org/10.4067/S0716-09172014000200003

L. A. Zade, “Fuzzy sets”, Information and Control, vol. 98, no. 3, pp. 338-353, 1965. https://doi.org/10.1016/S0019-9958(65)90241-X

Published

2022-09-13

How to Cite

[1]
T. Jalal and I. A. Malik, “I-convergent triple fuzzy normed spaces”, Proyecciones (Antofagasta, On line), vol. 41, no. 5, pp. 1093-1109, Sep. 2022.

Issue

Section

Artículos