Fibonacci Lacunary Statistical Convergence In Intuitionistic Fuzzy Normed Linear Spaces
Keywords:
Lacunary sequence, Fibonacci lacunary statistical convergence, intuitionistic fuzzy normed linear space
Abstract
We investigate the concept of Fibonacci lacunary statistical convergence in intuitionistic fuzzy normed linear spaces. We also introduce here a new concept, that is, Fibonacci lacunary statistical completeness and show that every intuitionistic fuzzy normed linear space is Fibonacci lacunary statistically complete.
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References
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[27] V.A. Khan, E.E. Kara, H. Altaf, N. Khan and M. Ahmad, Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces, J. Inequal. Appl. 202 (2019) 7 pages.
[28] M. Ilkhan and E. E. Kara, A new Banach space defined by Euler totient matrix operator, Operators and Matrices, 13(2) (2019) 527-544.
[29] N. Turan, E. E. Kara and M. Ilkhan, Quasi statistical convergence in cone metric spaces, Facta Univ. (NIS) Ser. Math. Inform. 33(4) (2018) 613-626.
[30] M. Ilkhan and E. E. Kara, A new type of statistical Cauchy sequence and its relation to Bourbaki completeness, Cogent Mathematics and Statistics 5 (2018) 9 pages.
[31] E. E. Kara and M. Ilkhan, Lacunary I-convergent and lacunary I-bounded sequence spaces defined by an Orlicz function, Electr. J. Math. Anal. Appl. 4 (2) (2016) 150-159.
[32] E. E. Kara and M. Ilkhan, On some Banach sequence spaces derived by a new band matrix, British J. Math. Comput. Sci. 9 (2) (2015) 141-159.
[33] E. E. Kara, M. Ba¸sar¨r and M. Mursaleen, Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers. Kragujev. J. Math. 39 (2) (2015) 217-230.
[34] E. E. Kara and S. Demiriz, Some new paranormed difference sequence spaces derived by Fibonacci numbers, Miskolc Math. Notes 16 (2) (2015) 907-923.
[35] E. E. Kara and M. Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra 64 (11) (2016), 2208-2223.
[36] A. Alotaibi, M. Mursaleen, BAS Alamri, S.A Mohiuddine, Compact operators on some Fibonacci difference sequence spaces. J. Inequal. Appl. 203 (2015) doi:10.1186/s13660-015-0713-5
[37] M. Candan, A new approach on the spaces of generalized Fibonacci di§erence null and convergent sequences, Math. Æterna 5 (1) (2015) 191-210.
[38] S. Demiriz, E. E. Kara and M. Ba¸sarır, On the Fibonacci almost convergent sequence space and Fibonacci core, Kyungpook Math. J. 55 (2015) 355-372.
[39] M. Kiri¸sçi and A. Karaisa, Fibonacci statistical convergence and Korovkin type approximation theorems, J. Ineq. Appl. 229 (2017) doi: doi:10.1186/s13660-017-1503-z
[40] M. Kiri¸sçi, Fibonacci statistical convergence on intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Systems, 36 (2019) 5597-5604.
[41] Ki¸si, I. Tuzcuoğlu, Fibonacci lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces, in press.
[42] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960) 314-334.
[2] J. A. Fridy, On statistical convergence, Analysis 5 (1985) 301-313.
[3] T. Salat, On statistical convergence of real numbers, Math. Slovaca 30 (1980) 139-150.
[4] J. A. Fridy and C. Orhan, Lacunary statistical convergence, Pacific. J. Math. 160 (1993) 43-51.
[5] S. Gahler, Linear-2-normierte Raume, Math. Nachr. 28 (1965) 1-43.
[6] A. White and Jr. George, 2-Banach spaces, Math. Nachr., 42 (1969) 43-60.
[7] S. Gahler, Untersuchungen uber verallgemeinerte m-metrische Raume, I, II, III, Math. Nachr. 40 (1969) 165-189.
[8] A. H. Siddiqi, 2-normed spaces, Aligarh Bull. math. (1980) 53-70.
[9] L. A. Zadeh, Fuzzy sets, Inform. Control 8 (1965) 338-353.
[10] A. K. Katsaras, Fuzzy topological vector spaces, Fuzzy Sets and Systems 12 (1984) 143-154.
[11] C. Felbin, Finite dimensional fuzzy normed linear spaces, Fuzzy Sets and Systems 48 (1992) 239-248.
[12] O. Kaleva and S. Seikkala, On fuzzy metric spaces, Fuzzy Sets and Systems 12 (1984) 215-229.
[13] K.T. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1) (1986) 87-96.
[14] J. H. Park, Intuitionistic fuzzy metric spaces, Chaos, Solitons and Fract. 22 (2004) 1039-1046.
[15] R. Saadati and J. H. Park, On the intuitionistic fuzzy topological spaces, Chaos, Solitons and Fract. 27 (2006) 331-344.
[16] S. Karaku¸s, K. Demirci and O. Duman, Statistical convergence on intuitionistic fuzzy normed spaces, Chaos, Solitons and Fract. 35 (2008) 763-769.
[17] Alotaibi, A, On lacunary statistical convergence of double sequences with respect to the intuitionistic fuzzy normed spaces, Int. J. Contemp. Math. Sciences, 5(42) (2010), 2069-2078.
[18] M. Mursaleen and S. A. Mohiuddine, Statistical convergence of double sequences in intuitionistic fuzzy normed space, Chaos, Solitons and Fract. 41 (5) (2009) 2414-2421.
[19] M. Mursaleen and S. A. Mohiuddine, On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space, J. Comp. Appl. Math. 233 (2) (2009) 142-149.
[20] E. Sava¸s and M. Gürdal, Certain summability methods in intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Syst. 27 (4) (2014)
[21] E. Sava¸s and M. Gürdal, A generalized statistical convergence in intuitionistic fuzzy normed spaces, Science Asia 41 (2015) 289-294.
[22] P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl. 63 (3) (2012) 708-715.
[23] S. Goonatilake, S: Toward a Global Science, p. 126. Indiana University Press, (1998).
[24] T. Koshy, Fibonacci and Lucas Numbers with Applications. Wiley, New York (2001).
[25] E.E. Kara and M. Ba¸sarir, An application of Fibonacci numbers into inÖnite Toeplitz matrices, Caspian J. Math. Sci. 1(1) (2012) 43-47.
[26] E.E. Kara, Some topological and geometrical properties of new Banach sequence spaces, J. Ineq. Appl. (38) (2013) 15. doi: 10.1186/1029-242X-2013-38.
[27] V.A. Khan, E.E. Kara, H. Altaf, N. Khan and M. Ahmad, Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces, J. Inequal. Appl. 202 (2019) 7 pages.
[28] M. Ilkhan and E. E. Kara, A new Banach space defined by Euler totient matrix operator, Operators and Matrices, 13(2) (2019) 527-544.
[29] N. Turan, E. E. Kara and M. Ilkhan, Quasi statistical convergence in cone metric spaces, Facta Univ. (NIS) Ser. Math. Inform. 33(4) (2018) 613-626.
[30] M. Ilkhan and E. E. Kara, A new type of statistical Cauchy sequence and its relation to Bourbaki completeness, Cogent Mathematics and Statistics 5 (2018) 9 pages.
[31] E. E. Kara and M. Ilkhan, Lacunary I-convergent and lacunary I-bounded sequence spaces defined by an Orlicz function, Electr. J. Math. Anal. Appl. 4 (2) (2016) 150-159.
[32] E. E. Kara and M. Ilkhan, On some Banach sequence spaces derived by a new band matrix, British J. Math. Comput. Sci. 9 (2) (2015) 141-159.
[33] E. E. Kara, M. Ba¸sar¨r and M. Mursaleen, Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers. Kragujev. J. Math. 39 (2) (2015) 217-230.
[34] E. E. Kara and S. Demiriz, Some new paranormed difference sequence spaces derived by Fibonacci numbers, Miskolc Math. Notes 16 (2) (2015) 907-923.
[35] E. E. Kara and M. Ilkhan, Some properties of generalized Fibonacci sequence spaces, Linear Multilinear Algebra 64 (11) (2016), 2208-2223.
[36] A. Alotaibi, M. Mursaleen, BAS Alamri, S.A Mohiuddine, Compact operators on some Fibonacci difference sequence spaces. J. Inequal. Appl. 203 (2015) doi:10.1186/s13660-015-0713-5
[37] M. Candan, A new approach on the spaces of generalized Fibonacci di§erence null and convergent sequences, Math. Æterna 5 (1) (2015) 191-210.
[38] S. Demiriz, E. E. Kara and M. Ba¸sarır, On the Fibonacci almost convergent sequence space and Fibonacci core, Kyungpook Math. J. 55 (2015) 355-372.
[39] M. Kiri¸sçi and A. Karaisa, Fibonacci statistical convergence and Korovkin type approximation theorems, J. Ineq. Appl. 229 (2017) doi: doi:10.1186/s13660-017-1503-z
[40] M. Kiri¸sçi, Fibonacci statistical convergence on intuitionistic fuzzy normed spaces, J. Intell. Fuzzy Systems, 36 (2019) 5597-5604.
[41] Ki¸si, I. Tuzcuoğlu, Fibonacci lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces, in press.
[42] B. Schweizer and A. Sklar, Statistical metric spaces, Pacific J. Math. 10 (1960) 314-334.
Published
2020-07-21
How to Cite
Kişi, Ömer, & Tuzcuoğlu, I. (2020). Fibonacci Lacunary Statistical Convergence In Intuitionistic Fuzzy Normed Linear Spaces. Journal of Progressive Research in Mathematics, 16(3), 3001-3007. Retrieved from https://scitecresearch.com/journals/index.php/jprm/article/view/1880
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