TARU PUBLICATIONS
Journal of Interdisciplinary Mathematics cover
Hybrid ·Peer-reviewed·ISSN (Online): 2169-012X·ISSN (Print): 0972-0502

Monthly Journal: Publishes the methodological and theoretical role of mathematics and mathematical applications underpinning scientific research.

Issues up to 2022 co-published with and available at:Taylor & Francis Online
submissions@tarupublications.com
Open Access Research Article

Fibonacci statistical convergence of double sequences of order  α–  in intuitionistic fuzzy normed spaces (IFNS)

* ,

* Corresponding author · click or hover a name for details

pp. 1817–1826Vol. 27Issue 8December 2024DOI: 10.47974/JIM-2046XML
Received:
10 Jul 2024
Published Online:
16 Dec 2024
Article type:
Research Article
Language:
EN
Article no.:
JIM-2046
Pages:
1817–1826

Abstract

The main objective of this work is to study and develop the theory of Fibonacci statistical convergence of double sequences of order α– in IFNS. We examine the Fibonacci statistically Cauchy double sequences of order α– and Fibonacci statistically completeness of double sequences of order α– in IFNS.

Keywords

Subject Classifications

40A3540A05

References

[1] H. Fast, “Sur la convergence statistique,” Colloq. Math., vol. 2, pp. 241–244 (1951).
[2] I. J. Schoenberg, “The integrability of certain functions and related summability methods,” Amer. Math. Monthly, vol. 66, pp. 361–375 (1959).
[3] M. Mursaleen and O. H. H. Edely, “Statistical convergence of double sequences,” J. Math. Anal. Appl., vol. 288, pp. 223–231 (2003).
[4] L. A. Zadeh, “Fuzzy sets,” Inform. Control, vol. 8, pp. 338–353 (1965).
[5] K. T. Atanassov, “Intuitionistic fuzzy sets,” Fuzzy Sets and Systems, vol. 20, no. 1, pp. 87–96 (1986).
[6] J. H. Park, “Intuitionistic fuzzy metric spaces,” Chaos Solitons Fractals, vol. 22, pp. 1039–1046 (2004).
[7] R. Saadati, “On the intuitionistic fuzzy topological spaces,” Chaos Solitons Fractals, vol. 27, pp. 331–344 (2006).
[8] S. Karakuş, “Statistical convergence on intuitionistic fuzzy normed spaces,” Chaos Solitons Fractals, vol. 35, pp. 763–769 (2008).
[9] M. Mursaleen, “Statistical convergence of double sequences in intuitionistic fuzzy normed space,” Chaos Solitons Fractals, vol. 41, no. 5, pp. 2414–2421 (2009).
[10] M. Mursaleen, “On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space,” J. Comp. Appl. Math., vol. 233, no. 2, pp. 142–149 (2009).
[11] E. Savaş, “Certain summability methods in intuitionistic fuzzy normed spaces,” J. Intell. Fuzzy Syst., vol. 27, no. 4, pp. 1621–1629 (2014).
[12] E. Savaş, “A generalized statistical convergence in intuitionistic fuzzy normed spaces,” Science Asia, vol. 41, pp. 289–294 (2015).
[13] P. Debnath, “Lacunary ideal convergence in intuitionistic fuzzy normed linear space,” Comput. Math. Appl., vol. 63, no. 3, pp. 708–715 (2012).
[15] E. E. Kara, “Some topological and geometrical properties of new Banach sequence space,” J. Inequal. Appl., vol. 38 (2013).
[16] V. A. Khan, “Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces,” J. Inequal. Appl., vol. 202, p. 7 (2019).
[17] M. İlkan, “A new Banach space defined by Euler totient matrix operator,” Operators and Matrices, vol. 13, no. 2, pp. 527–544 (2019).
[18] E. E. Kara, “On some Banach sequence spaces derived by a new band matrix,” British J. Math. Comput. Sci., vol. 9, no. 2, pp. 141–159 (2015).
[19] E. E. Kara, “Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers,” Kragujev. J. Math., vol. 39, no. 2, pp. 217–230 (2015).
[20] E. E. Kara, “Some new paranormed difference sequence spaces derived by Fibonacci numbers,” Miskolc Math. Notes, vol. 16, no. 2, pp. 907–923 (2015).
[21] E. E. Kara, “Some properties of generalized Fibonacci sequence space,” Linear Multilinear Algebra, vol. 64, no. 11, pp. 2208–2223 (2016).
[22] A. Alotaibi, “Compact operators on some Fibonacci difference sequence space,” J. Inequal. Appl., vol. 203 (2015).
[23] S. Demiriz, “On the Fibonacci almost convergent sequence space and Fibonacci core,” Kyungpook Math. J., vol. 55, pp. 355–372 (2015).
[24] M. Kirişci, “Fibonacci statistical convergence and Korovkin type approximation theorems,” J. Inequal. Appl., vol. 229 (2017).
[25] M. Kirişci, “Fibonacci statistical convergence on intuitionistic fuzzy normed spaces,” J. Intell. Fuzzy Syst., vol. 36, pp. 5597–5604 (2019).
[26] O. Kisi, “Fibonacci lacunary statistical convergence in intuitionistic fuzzy normed linear spaces,” unpublished (2019).
[27] R. Çolak, “Statistical convergence of order α,” in Modern Methods in Analysis and Its Applications, Anamaya Publishers, New Delhi, India, pp. 121–129 (2010).
[28] O. Kisi, “On Fibonacci lacunary statistical convergence of double sequences in intuitionistic fuzzy normed linear spaces,” Int. J. Adv. Appl. Math. Mech., vol. 7, no. 4, pp. 64-71 (2020). 
[29] G. N.Bilgin, “Fibonacci lacunary statistical convergence of order gamma in IFNLS,” Int. J. Adv. Appl. Math. and Mech., vol. 8(4), pp. 28- 36 (2021). 
[30] A. Alotaibi, “ On lacunary statistical convergence of double sequenc­es with respect to the intuitionistic fuzzy normed spaces,” Int. J. Con­temp. Math. Sciences, vol. 5(42), pp. 2069-2078 (2010). 

Views: 206Downloads: 84Citations: 0