Fibonacci Lacunary Ideal Convergence of Double Sequences in Intuitionistic Fuzzy Normed Linear Spaces

The purpose of this article is to research the concept of Fibonacci lacunary ideal convergence of double sequences in intuitionistic fuzzy normed linear spaces (IFNS). Additionally, a new concept, called Fibonacci lacunary convergence, is examined. Also, Fibonacci lacunary I₂-limit points and Fibonacci lacunary I₂-cluster points for double sequences in IFNS have been defined and the significant results have been given. Additionally, Fibonacci lacunary Cauchy and Fibonacci lacunary I₂-Cauchy double sequences are worked.

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  • [1] Atanassov, K.T.: Intuitionistic fuzzy sets. Fuzzy Sets and Syst. 20, 87-96 (1986).
  • [2] Debnath, P.: Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces. Comput. Math. Appl. 63, 708-715 (2012).
  • [3] Dündar, E., Ulusu, U., Pancarog ̆lu, N.: Strongly I2-lacunary convergence and I2-lacunary Cauchy double sequences of sets. Aligarh Bull. Math. 35 (1-2), 1-15 (2016).
  • [4] Dündar, E., Ulusu, U., Aydın, B.: I2-lacunary statistical convergence of double sequences of sets. Konuralp J. Math. 5 (1), 1-10 (2017).
  • [5] Fast, H.: (1951). Sur la convergence statistique. Colloq. Math. 2, 241-244 (1951).
  • [6] Fridy, J.A., Orhan, C.: Lacunary statistical convergence. Pacific J. Math. 160 (1), 43-51 (1993).
  • [7] Goonatilake S.: Toward a Global Science. Indiana University Press. (1998).
  • [8] Hazarika, B.: Lacunary ideal convergence of multiple sequences. J. Egyptian Math. Soc. 24, 54-59 (2016).
  • [9] Kara, E.E., Bas ̧arır, M.: An application of Fibonacci numbers into infinite Toeplitz matrices. Casp. J. Math. Sci. 1 (1), 43-47 (2012).
  • [10] Kara, E.E.: Some topological and geometrical properties of new Banach sequence spaces. J. Inequal. Appl. 38 (2013), (2013).
  • [11] Karakus ̧, S., Demirci, K., Duman, O.: Statistical convergence on intuitionistic fuzzy normed spaces. Chaos Solitons Fractals. 35, 763-769 (2008).
  • [12] Kirişçi, M., Karaisa, A.: Fibonacci statistical convergence and Korovkin type approximation theorems. J. Inequal. Appl. 2017 (229), 1-15 (2017).
  • [13] Kişi, Ö., Tuzcuog ̆lu, I.: Fibonacci lacunary statistical convergence in intuitionistic fuzzy normed linear spaces. J. Progress Res. Soc. Sci. 16 (3), 3001-3007 (2020).
  • [14] Kis ̧i, Ö., Güler, E.: On Fibonacci ideal convergence of double sequences in intuitionistic fuzzy normed linear spaces. Turk. J. Math. Comput. Sci. 11, 46-55 (2019).
  • [15] Koshy, T.: Fibonacci and Lucas Numbers with Applications. Wiley, New York. (2001).
  • [16] Kostyrko, P., Salat, T., Wilczynsski, W.: I-convergence. Real Anal. Exchange. 6 (2), 669-686 (2001).
  • [17] Mursaleen, M., Edely, O.H.: Statistical convergence of double sequences. J. Math. Anal. Appl. 288, 223-231 (2003).
  • [18] Mursaleen, M., Mohiuddine, S.A.: Statistical convergence of double sequences in intuitionistic fuzzy normed space. Chaos Solitons Fractals. 41, 2414-2421 (2009).
  • [19] Mursaleen, M., Mohiuddine, S.A., Edely, O.H.H.: On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces. Comput. Math. Appl. 59, 603-611 (2010).
  • [20] Mursaleen, M., Mohiuddine, S.A.: On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space. J. Comput. Appl. Math. 233 (2), 142-149 (2009).
  • [21] Nuray, F., Ulusu, U., Dündar, E.: Lacunary statistical convergence of double sequences of sets. Soft Comput. 20, 2883-2888 (2016).
  • [22] Park, J.H.: Intuitionistic fuzzy metric spaces. Chaos Solitons Fractals. 22, 1039-1046 (2004).
  • [23] Lael, F., Nourouzi, K.: Some results on the IF-normed spaces. Chaos Solitons Fractals. 37, 931-939 (2008).
  • [24] Savas ̧, E., Patterson, R.F.: Lacunary statistical convergence of double sequences. Math. Commun. 10, 55-61 (2005).
  • [25] Schweizer, B., Sklar, A.: Statistical metric spaces. Pacific J. Math. 10, 314-334. (1960).
  • [26] Temizer Ersoy, M., Furkan, H.: Distinguished supspaces in topological sequence spaces theory. AIMS Math. 5 (4), 2858-2868 (2020).
  • [27] Temizer Ersoy, M.: Some abelian, tauberian and core theorems related to the (V, λ) summability. Univers. J. Math. Appl. 4 (2), 70-75.
  • [28] Tripathy,B.C.,Hazarika,B.,Choudhary,B.B.:LacunaryI-convergentsequences.KyungpookMath.J.2(4),473-482 (2012).
  • [29] Tripathy, B.K., Tripathy, B.C.: On I-convergent double sequences. Soochow J. Math. 31 (4), 549-560 (2005).
  • [30] Zadeh, L.A.: Fuzzy sets. Inf.Control. 8, 338-353 (1965). (2021).
Mathematical Sciences and Applications E-Notes-Cover
  • ISSN: 2147-6268
  • Yayın Aralığı: Yılda 4 Sayı
  • Başlangıç: 2013
  • Yayıncı: -