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Dergiler / Turkish Journal of Mathematics and Computer Science / 2026 / Volume: 11 Special Issue

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

Ömer Kişi(Deparment of Mathematics, Bartın University, Bartın, Turkey.)0000-0001-6844-3092
Erhan Güler0000-0003-3264-6239
Sayfa
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Yayın Tarihi
2019-12-30
DOI
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⚡ TL;DR(1 Cümlede Hızlı Çıkarım)

We define the Fibonacci $\mathcal{I}_{2}$-Cauchy sequences and the Fibonacci $% \mathcal{I}_{2}$ completeness with respect to an intuitionistic fuzzy normed linear space.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:The aim of this article is to introduce and study the notion of Fibonacci $% \mathcal{I}_{2}$-convergence on intuitionistic fuzzy normed linear space.
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Temel Bulgular & Veri:The aim of this article is to introduce and study the notion of Fibonacci $% \mathcal{I}_{2}$-convergence on intuitionistic fuzzy normed linear space.
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Sonuç & Katkı:We define the Fibonacci $\mathcal{I}_{2}$-Cauchy sequences and the Fibonacci $% \mathcal{I}_{2}$ completeness with respect to an intuitionistic fuzzy normed linear space.
🔬Tür:Conference Paper
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Fibonacci I₂-convergence · Fibonacci I₂-Cauchy sequence · intuitionistic fuzzy normed linear space

Abstract

The aim of this article is to introduce and study the notion of Fibonacci $% \mathcal{I}_{2}$-convergence on intuitionistic fuzzy normed linear space. We define the Fibonacci $\mathcal{I}_{2}$-Cauchy sequences and the Fibonacci $% \mathcal{I}_{2}$ completeness with respect to an intuitionistic fuzzy normed linear space.

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Bu Makaleye Atıf Yap

Kişi, Ö., Güler, E. (2019). On Fibonacci Ideal Convergence of Double Sequences in Intuitionistic Fuzzy Normed Linear Spaces. Turkish Journal of Mathematics and Computer Science, Volume: 11 Special Issue. https://ajindex.com/articles/1324870

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Kaynakça (51)

  1. Anastassiou, G.A., {\em Fuzzy approximation by fuzzy convolution type operators}, Comput. Math. Appl., \textbf{48}(2004), 1369--1386.
  2. Arslan M., D\"{u}ndar E., \textit{$\mathcal{I}$-convergence and $% \mathcal{I}$-Cauchy sequence of functions in 2-normed spaces}, Konuralp J. Math., \textbf{6:1}(2018), 57-- 62.
  3. Atanassov, K.T., \textit{Intuitionistic fuzzy sets}, Fuzzy Sets Syst., \textbf{20}(1986), 87--96.
  4. Atanassov, K., Pasi, G., Yager, R., Intuitionistic fuzzy interpretations of multi-person multicriteria decision making, in: Proceedings of 2002 First International IEEE Symposium Intelligent Systems, \textbf{1}(2002), 115-119.
  5. Bakery, A.A.,\textit{ Operator ideal of Cesaro type sequence spaces involving lacunary sequence,} Abst. Appl. Anal, \textbf{2014}(2014), 6 pp., Article ID 419560, http://dx.doi.org/10.1155/2014/419560.
  6. Bakery, A.A., Mohammed, M.M., \textit{On lacunary mean ideal convergence in generalized random $n$-normed spaces}, Abstract Appl. Anal., \textbf{2014}(2014), 11 pp., Article ID:101782, http://dx.doi.org/10.1155/2014/101782.
  7. Barros, L.C., Bassanezi, R.C., Tonelli, P.A., \textit{Fuzzy modelling in population dynamics}, Ecol Model, \textbf{128}(2000), 27--33.
  8. Debnath, P., \textit{Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces}, Comput. Math. Appl., \textbf{63}(2012), 708--715.
  9. D\"{u}ndar E., Altay B., \textit{$\mathcal{I}_{2}$-convergence and $% \mathcal{I}_{2}$-Cauchy of double sequences}, Acta Math. Sci., \textbf{34B(2)}(2014), 343--353.
  10. El Naschie, M.S.,\textit{ On the unification of heterotic strings, $% m$-theory and $\epsilon ^{\infty }$-theory}, Chaos Solitons Fractals, \textbf{11}(2000), 2397--2408.
  11. Erceg, M.A., \textit{Metric spaces in fuzzy set theory}, J. Math. Anal. Appl., \textbf{69}(1979), 205--230.
  12. Fast, H., \textit{Sur la convergence statistique}, Colloq. Math., \textbf{2}(1951), 241--244.
  13. Fradkov, A.L., Evans, R.J., \textit{Control of chaos: methods and applications in engineering}, Chaos Solitons Fractals, \textbf{29}(1) (2005), 33--56.
  14. Fridy, J.A., Orhan, C., \textit{Lacunary statistical convergence}, Pacific J. Math., \textbf{160(1)}(1993), 43--51.
  15. Fridy, J.A., Orhan, C., \textit{Lacunary statistical summability}, J. Math. Anal Appl., \textbf{173}(1993), 497--504.
  16. George, A., Veeramani P., \textit{On some results in fuzzy metric spaces}, Fuzzy Sets Syst., \textbf{64(3)}(1994), 395--399.
  17. Giles, R., \textit{A computer program for fuzzy reasoning}, Fuzzy Sets Syst., \textbf{4}(1980), 221--234.
  18. Goonatilake, S., Toward a Global Science, p. 126, Indiana University Press, (1998).
  19. Hazarika, B., \textit{ Lacunary $\mathcal{I}$-convergent sequence of fuzzy real numbers}, Pacific J. Sci. Technol., \textbf{10(2)}(2009), 203--206.
  20. Hazarika, B., \textit{Fuzzy real valued lacunary $\mathcal{I}$% -convergent sequences}, Appl. Math. Lett., \textbf{25}(2012), 466--470.
  21. Hazarika, B., \textit{Lacunary ideal convergent double sequences of fuzzy real numbers}, J. Intell. Fuzzy Syst. \textbf{27(1)}(2014), 495--504.
  22. Hazarika, B., \textit{Lacunary ideal convergence of multiple sequences}, J. Egyptian Math. Soc., \textbf{24(1)}(2016), 54--59.
  23. Hong, L., Sun, J.Q., \textit{Bifurcations of fuzzy nonlinear dynamical systems}, Commun. Nonlinear Sci. Numer. Simul., \textbf{1}(2006), 1--12.
  24. Hosseini, S.B., O'Regan, D., Saadati, R., \textit{Some results of intuitionistic fuzzy spaces}, Iranian J. Fuzzy Syst., \textbf{4(1)}(2007), 53--64.
  25. J\"{a}ger, G., \textit{Fuzzy uniform convergence and equicontinuity}, Fuzzy Sets Syst., \textbf{109}(2000), 187--198.
  26. Kaleva, O., Seikkala, S., \textit{On fuzzy metric spaces}, Fuzzy Sets Syst., \textbf{12}(1984), 215--229.
  27. Kara, E.E., Ba\c{s}ar\i r, M., \textit{An application of Fibonacci numbers into infinite Toeplitz matrices}, Caspian J. Math. Sci., \textbf{1(1)}(2012), 43--47.
  28. Kara, EE., \textit{Some topological and geometrical properties of new Banach sequence spaces}, J. Inequal. Appl., \textbf{38}(2013), doi:10.1186/1029-242X-2013-38.
  29. Karakus, S., Demirci, K., Duman, O., \textit{Statistical convergence on intuitionistic fuzzy normed spaces}, Chaos Solitons Fractals, \textbf{35}(2008), 763--769.
  30. Kiri\c{s}\c{c}i, M, \textit{Fibonacci statistical convergence on intuitionistic fuzzy normed spaces}, J. Intell Fuzzy Syst, \textbf{36(6)}(2019), 5597--5604.
  31. Kiri\c{s}\c{c}i, M, Karaisa, A., \textit{Fibonacci statistical convergence and Korovkin type approximation theorems}, J. Inequal. Appl., \textbf{229}(2017), doi: 10.1186/s13660-017-1503-z.
  32. Kocinac, Lj.D.R., Khan, V.A., Alshlool, K.M.A.S., Altaf, H., \textit{On some topological properties of intuitionistic 2-fuzzy n-normed linear spaces}, Hacet. J. Math. Stat., in press.
  33. Kocinac, Lj.D.R., Rashid, M.H.M., \textit{On ideal convergence of double sequences in the topology induced by a fuzzy 2-norm}, TWMS J. Pure Appl. Math., \textbf{8:1}(2017), 97--111.
  34. Koshy, T., Fibonacci and Lucas Numbers with Applications, Wiley, New York. 2001.
  35. Kostyrko, P., Salat, T., Wilczynsski, W., \textit{$\mathcal{I}$% -convergence}, Real Anal. Exchange, \textbf{26(2)}(2000-2001), 669--686.
  36. Li, J., \textit{Lacunary statistical convergence and inclusion properties between lacunary methods}, Int. J Math. Math. Sci., \textbf{23(3)}(2000), 175--180.
  37. Madore, J., \textit{Fuzzy physics}, Ann. Phys., \textbf{219}(1992), 187--198.
  38. Mohiuddine, S.A., Alghamdi, M.A., \textit{Statistical summability through lacunary sequence in locally solid Riesz spaces}, J. Ineq Appl., \textbf{225}(2012), 1--9.
  39. Mursaleen, M., Mohiuddine, S.A., \textit{Statistical convergence of double sequences in intuitionistic fuzzy normed space}, Chaos Solitons Fractals, \textbf{41}(2009), 2414--2421.
  40. Mursaleen, M., Mohiuddine, S.A., \textit{On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space}, J. Comput. Appl. Math., \textbf{233(2)}(2009), 142--149.
  41. Mursaleen, M., Mohiuddine, S.A., Edely, H.H., \textit{On the ideal convergence of double sequences in intuitionistic fuzzy normed spaces}, Comput. Math. Appl., \textbf{59}(2010), 603--611.
  42. Narayanan, A., Vijayabalaji, S., Thillaigovindan, N. \textit{Intuitionistic fuzzy bounded linear operators}, Iranian J. Fuzzy Syst., \textbf{4}(2007), 89--101.
  43. Park, J.H., \textit{Intuitionistic fuzzy metric spaces}, Chaos Solitons Fractals, \textbf{22}(2004), 1039--1046.
  44. Saadati, R., Park, J.H., \textit{On the intuitionistic fuzzy topological spaces}, Chaos Solitons Fractals, \textbf{27}(2006), 331--344.
  45. Salat, T., Tripathy, B.C., Ziman, M., \textit{On some properties of $% \mathcal{I}$-convergence}, Tatra Mt. Math Publ., \textbf{28}(2004), 279--286.
  46. Schoenberg, I.J., \textit{The integrability of certain functions and related summability methods}, Am. Math. Mon., \textbf{66}(1959), 361--375.
  47. Sen, M., Debnath P., \textit{Lacunary statistical convergence in intuitionistic fuzzy $n$-normed linear spaces}, Math. Comput. Modelling, \textbf{54}(2011), 2978--2985.
  48. Tripathy, B.C., Hazarika, B., \textit{$\mathcal{I}$% -monotonic and $\mathcal{I}$-convergent sequences}, Kyungpook Math. J., \textbf{51}(2011), 233--239.
  49. Tripathy, B.C., Hazarika, B., Choudhary, B., \textit{Lacunary $\mathcal{I}$-convergent sequences}, Kyungpook Math. J., \textbf{52(4)}(2012), 473--482.
  50. Wu, K., \textit{Convergences of fuzzy sets based on decomposition theory and fuzzy polynomial function}, Fuzzy Sets Syst., \textbf{109}(2000), 173--185.
  51. Zadeh, L.A.,\textit{ Fuzzy sets}, Inf. Control., \textbf{8}(1965), 338--353.