On Δᵐ-statistical convergence double sequences in intuitionistic fuzzy normed spaces

• Antal, Reena ; Chawla, Meenakshi ; Kumar, Vijay ; Hazarika, Bipan ^[1]
  1. [1] Gauhati University

     Gauhati University

     India

     
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 3, 2022, págs. 697-713
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4633
• Enlaces
  • Texto completo
• Resumen

  • In the present paper, the basic objective of our work is to define Δᵐ-statistical convergence in the setup of intuitionistic fuzzy normed spaces for double sequences. We have proved some examples which shows this method of convergence is more generalized. Further, we defined the Δᵐ-statistical Cauchy sequences in these spaces and given the Cauchy convergence criterion for this new notion of convergence.

• Referencias bibliográficas
  • R. Antal, M. Chawla, V. Kumar, “Statistical Λ-convergence in intuitionistic fuzzy normed spaces”, Buletinul Academiei de Stiinte a Republicii...
  • R. Antal, M. Chawla, V. Kumar, “Generalized statistical convergence of order α in random n-normed space”, Advances and Applications in Mathematical...
  • M. Chawla, M. S. Saroa, and V. Kumar, “On Δᵐ-statistical convergence of order ∝ in random 2-normed space”, Miskolc Mathematical Notes, vol....
  • M. Chawla and Palak, “Lacunary statistical convergence of double sequences of order α in probabilistic normed spaces”, Advances in Mathematics:...
  • A. Esi, “On some new generalized difference double sequence spaces defined by Orlicz functions”, Matematika, vol. 27, pp. 31-40, 2011.
  • A. Esi and M. Kemal Ozdemir, “Generalized Δᵐ-Statistical convergence in probabilistic normed space”, Journal of Computational Analysis and...
  • M. Et and R. Çolak, “On some generalized difference sequence spaces”, Soochow Journal of Mathematical, vol. 21, no. 4, pp. 377-386, 1995
  • M. Et, F. Nuray, “Δᵐ-Statistical convergence”, Indian Journal of Pure and Applied Mathematics, vol. 32, no. 6, pp. 961-969, 2001.
  • H. Fast, “Sur La Convergence Statistique”, Colloquium Mathematicum, vol. 2, no. 3-4, pp. 241–244, 1951. https://doi.org/10.4064/cm-2-3-4-241-244
  • J. A. Fridy, “On statistical convergence”, Analysis, vol. 5, no. 4, pp. 301–313, 1985. https://doi.org/10.1524/anly.1985.5.4.301
  • B. Hazarika, “Lacunary generalized difference statistical convergence in random 2-normed spaces”, Proyecciones (Antofagasta), vol. 31, no....
  • B. Hazarika, A. Alotaibi, and S. A. Mohiuddine, “Statistical convergence in measure for double sequences of fuzzy-valued functions”, Soft...
  • S. Karakus, “Statistical convergence on probabilistic normed space”, Mathematical Communications, vol. 12, pp. 11-23, 2007. [Online] Available:...
  • S. Karakus, K. Demirci, and O. Duman, “Statistical convergence on intuitionistic fuzzy normed spaces”, Chaos, Solitons and Fractals, vol....
  • H. Kizmaz, “On certain sequence spaces”, Canadian Mathematical Bulletin, vol. 24, no. 2, pp. 169–176, 1981. https://doi.org/10.4153/cmb-1981-027-5
  • I. J. Maddox, “Statistical convergence in a locally convex space”, Mathematical Proceedings of the Cambridge Philosophical Society, vol. 104,...
  • S. A. Mohiuddine and Q. M. Danish Lohani, “On generalized statistical convergence in intuitionistic fuzzy normed space”, Chaos, Solitons and...
  • S. A. Mohiuddine, B. Hazarika, and A. Alotaibi, “On statistical convergence of double sequences of fuzzy valued functions”, Journal of Intelligent...
  • F. Móricz, “Statistical convergence of multiple sequences”, Archiv der Mathematik, vol. 81, no. 1, pp. 82–89, 2003. https://doi.org/10.1007/s00013-003-0506-9
  • M. Mursaleen, A. K. Noman, “On the spaces of λ-convergent and bounded sequences”, Thai Journal of Mathematics, vol. 8, no. 2, pp. 311-329,...
  • M. Mursaleen and S. A. Mohiuddine, “On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space”, Journal of...
  • M. Mursaleen and S. A. Mohiuddine, “Statistical convergence of double sequences in intuitionistic fuzzy normed spaces”, Chaos, Solitons and...
  • M. Mursaleen, O. H. H. Edely, “Statistical convergence of double sequences”, Journal of Mathematical Analysis and Applications, vol. 288,...
  • J. H. Park, “Intuitionistic fuzzy metric spaces”, Chaos, Solitons and Fractals, vol. 22, no. 5, pp. 1039–1046, 2004. https://doi.org/10.1016/j.chaos.2004.02.051
  • A. Pringsheim, “Zur Theorie der Zweifach Unendlichen zahlenfolgen”, Mathematische Annalen, vol. 53, no. 3, pp. 289–321, 1900. https://doi.org/10.1007/bf01448977
  • R. Saadati and J. H. Park, “On the intuitionistic fuzzy topological spaces”, Chaos, Solitons and Fractals, vol. 27, no. 2, pp. 331–344, 2006....
  • B. Schweizer and A. Sklar, “Statistical Metric Spaces”, Pacific Journal of Mathematics, vol. 10, no. 1, pp. 313–334, 1960. https://doi.org/10.2140/pjm.1960.10.313
  • M. Sen and M. Et, “Lacunary statistical and lacunary strongly convergence of generalized difference sequences in intuitionistic fuzzy normed...
  • B. C. Tripathy, B. Sarma, “On some classes of difference double sequence spaces”, Fasciculi Mathematici, vol. 41, pp. 135-142, 2009.
  • B. C. Tripathy and B. Sarma, “Statistically convergent difference double sequence spaces”, Acta Mathematica Sinica, English Series, vol. 24,...
  • B. C. Tripathy and S. Borgohain, “Statistically convergent difference sequence spaces of fuzzy real numbers defined by Orlicz function”, Thai...
  • B. C. Tripathy and M. Sen, “On lacunary strongly almost convergent double sequences of fuzzy numbers”, Annals of the University of Craiova...
  • B. C. Tripathy and R. Goswami, “Statistically convergent multiple sequences in probabilistic normed spaces”, University Politehnica of Bucharest...
  • B. C. Tripathy, “Statistically convergent double sequences”, Tamkang Journal of Mathematics, vol. 34, no. 3, pp. 231–237, 2003. https://doi.org/10.5556/j.tkjm.34.2003.314
  • L. A. Zadeh, “Fuzzy sets”, Information and Control, vol. 8, no. 3, pp. 338–353, 1965. https://doi.org/10.1016/s0019-9958(65)90241-x