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

Year 2022, Volume: 10 Issue: 3, 114 - 124, 09.09.2022

Ömer Kişi

https://doi.org/10.36753/mathenot.931071

Cited By: 1

Abstract

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.

Keywords

Fibonacci number, Fibonacci sequence, intuitionistic fuzzy normed linear space

References

• [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).