본문 바로가기
KERD
논문KCI 등재

Fibonacci lacunary statistical convergence in intuitionistic fuzzy $n$-normed linear spaces

Omer Kisi|Ibrahim Tuzcuoglu
기초자연과학연구소 (The Natural Science Institute Wonkwang University)|2020.12|ANNALS OF FUZZY MATHEMATICS AND INFORMATICS|제20권 제3호|pp. 207-222|DOI 10.30948/afmi.2020.20.3.207

1

조회

0

다운로드

0

인용

0

참고문헌

키워드

Lacunary sequenceFibonacci lacunary statistical convergenceFibonacci lacunary statistical Cauchy sequenceIntuitionistic fuzzy normed linear space

초록

In the current paper, we investigate the concept of Fibonacci lacunary statistical convergence in intuitionistic fuzzy $n$-normed linear spaces which removes any ambiguity that could arise from the previously defined notion of the same. Some inclusion relations between the sets of Fibonacci statistically convergent and Fibonacci lacunary statistically convergent sequences are examined in an intuitionistic fuzzy $n$-normed linear space. We also define Fibonacci lacunary statistical Cauchy sequence in an intuitionistic fuzzy $n$-normed linear space and prove that it is equivalent to Fibonacci lacunary statistically convergent sequence.

Abstract

In the current paper, we investigate the concept of Fibonacci lacunary statistical convergence in intuitionistic fuzzy $n$-normed linear spaces which removes any ambiguity that could arise from the previously defined notion of the same. Some inclusion relations between the sets of Fibonacci statistically convergent and Fibonacci lacunary statistically convergent sequences are examined in an intuitionistic fuzzy $n$-normed linear space. We also define Fibonacci lacunary statistical Cauchy sequence in an intuitionistic fuzzy $n$-normed linear space and prove that it is equivalent to Fibonacci lacunary statistically convergent sequence.

참고문헌 (68)

  1. A. Alotaibi, "Compact operators on some Fibonacci difference sequence spaces", J. Inequal. Appl., 203 (2015)[DOI]
  2. K. T. Atanassov, "Intuitionistic fuzzy sets", Fuzzy Sets and Systems, 20, pp.87~96 (1986)
  3. T. Bag, "Finite dimensional fuzzy normed linear spaces", J. Fuzzy Math, 11, pp.687~705 (2003)
  4. T. Bag, "Fuzzy bounded linear operators", Fuzzy Sets and Systems, 151, pp.513~547 (2005)
  5. M. Candan, "A new approach on the spaces of generalized Fibonacci difference null and convergent sequences", Math. Æterna, 5(1), pp.191~210 (2015)
  6. S. C. Chang, "Fuzzy linear operators and fuzzy normed linear spaces", Bull. Cal. Math. Soc, 86, pp.429~436 (1994)
  7. P. Debnath, "Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces", Comput. Math. Appl, 63(3), pp.708~715 (2012)
  8. P. Debnath, "Some completeness results in terms of infinite series and quotient spaces in intuitionistic fuzzy n-normed linear spaces", J. Intell. Fuzzy Syst, 26(2), pp.975~982 (2014)
  9. P. Debnath, "Some results of calculus for functions having values in an intuitionistic fuzzy n-normed linear space", J. Intell. Fuzzy Syst, 26(6), pp.2983~2991 (2014)
  10. P. Debnath, "Results on lacunary difference ideal convergence in intuitionistic fuzzy normed linear spaces", J. Intell. Fuzzy Syst, 28(3), pp.1299~1306 (2015)
  11. P. Debnath, "A generalised statistical convergence in intuitionistic fuzzy n-normed linear spaces", Ann. Fuzzy Math. Inform, 12(4), pp.559~572 (2016)
  12. Serkan Demiriz, "On the Fibonacci Almost Convergent Sequence Space and Fibonacci Core", Kyungpook Mathematical Journal, 55(2), pp.355~372 (2015), 경북대학교 자연과학대학 수학과
  13. H. Fast, "Sur la convergenc statistique", Colloq. Math, 2, pp.241~244 (1951)
  14. C. Felbin, "Finite dimensional fuzzy normed linear spaces", Fuzzy Sets and Systems, 48, pp.239~248 (1992)
  15. C. K. Felbin, "Finite dimensional fuzzy normed linear spaces II. p-adic analysis, summability theory, fuzzy analysis and applications (INCOPASFA) (Chennai, 1998)", J. Anal., 7, pp.117~131 (1999)
  16. J. A. Fridy, "On statistical convergence", Analysis, 5, pp.301~313 (1985)
  17. J. A. Fridy, "Lacunary statistical convergence", Pacific. J. Math, 160, pp.43~51 (1993)
  18. S. G¨ahler, "Linear-2-normierte Raume", Math. Nachr, 28, pp.1~43 (1965)
  19. S. Gahler, "Untersuchungen uber verallgemeinerte m-metrische Raume, I, II, III", Math. Nachr., 40, pp.165~189 (1969)
  20. S. Goonatilake, "S: Toward a Global Science", pp.126~ (1998), Indiana University Press
  21. H. Gunawan, "On n-normed spaces", Int. J. Math. Math. Sci, 27, pp.631~639 (2001)
  22. M. Gurdal, "Ideal Convergence in n-normed spaces and some new sequence spaces via n-norm", Journal of Fundamental Sciences, 4(1), pp.233~244 (2008)
  23. M. Ilkhan, "A new type of statistical Cauchy sequence and its relation to Bourbaki completeness", Cogent Mathematics and Statistics, 5, pp.9~ (2018)
  24. M. Ilkhan, "A new Banach space defined by Euler totient matrix operator", Operators and Matrices, 13(2), pp.527~544 (2019)
  25. O. Kaleva, "On fuzzy metric spaces", Fuzzy Sets and Systems, 12, pp.215~229 (1984)
  26. Emrah Evren Kara, "Some topological and geometrical properties of new Banach sequence spaces", Journal of Inequalities and Applications, (38), pp.15~ (2013), Springer Science and Business Media LLC[DOI]
  27. E. E. Kara, "An application of Fibonacci numbers into infinite Toeplitz matrices", Caspian J. Math. Sci, 1(1), pp.43~47 (2012)
  28. E. E. Kara, "Compactness of matrix operators on some sequence spaces derived by Fibonacci numbers", Kragujev. J. Math., 39(2), pp.217~230 (2015)
  29. E. E. Kara, "Some new paranormed difference sequence spaces derived by Fibonacci numbers", Miskolc Math. Notes, 16(2), pp.907~923 (2015)
  30. E. E. Kara, "On some Banach sequence spaces derived by a new band matrix", British J. Math. Comput. Sci, 9(2), pp.141~159 (2015)
  31. E. E. Kara, "Lacunary I-convergent and lacunary I-bounded sequence spaces defined by an Orlicz function", Electr. J. Math. Anal. Appl, 4(2), pp.150~159 (2016)
  32. E. E. Kara, "Some properties of generalized Fibonacci sequence spaces", Linear Multilinear Algebra, 64(11), pp.2208~2223 (2016)
  33. V. Karakaya, "Statistical convergence of sequences of functions in intuitionistic fuzzy normed spaces", Abstract and Applied Analysis, 2012, pp.1~19 (2012)[DOI]
  34. S. Karaku¸s, "Statistical convergence on intuitionistic fuzzy normed spaces", Chaos, Solitons and Fract, 35, pp.763~769 (2008)
  35. A. K. Katsaras, "Fuzzy topological vector spaces", Fuzzy Sets and Systems, 12, pp.143~154 (1984)
  36. V. A. Khan, "Intuitionistic fuzzy I-convergent Fibonacci difference sequence spaces", J. Inequal. Appl, 202, pp.7~ (2019)
  37. M. Kirisci, "Fibonacci statistical convergence and Korovkin type approximation theorems", J. Ineq. Appl., 229 (2017)[DOI]
  38. M. Kirisci, "Fibonacci statistical convergence on intuitionistic fuzzy normed spaces", J. Intell. Fuzzy Systems, 36, pp.5597~5604 (2019)
  39. N. Konwar, "Generalized I∆s r-statistical convergence in intuitionistic fuzzy normed linear space", Songklanakarin J Sci Technol, 40(3), pp.540~549 (2018)
  40. N. Konwar, "Continuity and Banach contraction principle in intuitionistic fuzzy n-normed linear spaces", J. Intell. Fuzzy Syst, 33(4), pp.2363~2373 (2017)
  41. N. Konwar, "Approximation of new bounded operators in intuitionistic fuzzy n-Banach spaces", J. Intell. Fuzzy Syst, 35(6), pp.6301~6312 (2018)
  42. N. Konwar, "Some new contractive conditions and related fixed point theorems in intuitionistic fuzzy n-Banach spaces", J. Intell. Fuzzy Syst, 34(1), pp.361~372 (2018)
  43. Nabanita Konwar, "$I_{\lambda}$-convergence in intuitionistic fuzzy $n$-normed linear space", ANNALS OF FUZZY MATHEMATICS AND INFORMATICS, 13(1), pp.91~107 (2017), 기초자연과학연구소[DOI]
  44. T. Koshy, "Fibonacci and Lucas Numbers with Applications" (2001), Wiley
  45. V. Kumar, "On (λ, µ)-statistical convergence of double sequences on intuitionistic fuzzy normed space", Filomat, 25(2), pp.109~120 (2011)
  46. R. Malceski, "Strong n-convex n-normed spaces", Mat. Bilten, 21, pp.81~102 (1997)
  47. M. Mursaleen, "Statistical convergence of double sequences in intuitionistic fuzzy normed space", Chaos, Solitons and Fract, 41(5), pp.2414~2421 (2009)
  48. M. Mursaleen, "On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space", J. Comp. Appl. Math, 233(2), pp.142~149 (2009)
  49. AL. Narayanan, "Fuzzy n-normed linear space", Int. J. Math. Math. Sci, 24, pp.3963~3977 (2005)
  50. AL. Narayanan, "Intuitionistic fuzzy bounded linear operators", Iranian J. Fuzzy Syst, 4, pp.89~101 (2007)
  51. J. H. Park, "Intuitionistic fuzzy metric spaces", Chaos, Solitons and Fract., 22, pp.1039~1046 (2004)
  52. R. Saadati, "On the intuitionistic fuzzy topological spaces", Chaos, Solitons and Fract, 27, pp.331~344 (2006)
  53. T. Salat, "On statistical convergence of real numbers", Math. Slovaca, 30, pp.139~150 (1980)
  54. E. Savas, "Certain summability methods in intuitionistic fuzzy normed spaces", J. Intell. Fuzzy Syst, 27(4), pp.1621~1629 (2014)
  55. E. Savas, "A generalized statistical convergence in intuitionistic fuzzy normed spaces", ScienceAsia, 41, pp.289~294 (2015)
  56. E. Savas, "Generalized statistically convergent sequences of functions in fuzzy 2-normed spaces", J. Intell. Fuzzy Syst, 27, pp.2067~2075 (2014)
  57. E. Savas, "Ideal convergent Function Sequences in Random 2-Normed spaces", Filomat, 30(3), pp.557~567 (2016)
  58. E. Savas, "I-lacunary statistical convergence of weighted g via modulus functions in 2-normed spaces", Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., 68(2), pp.2324~2332 (2019)
  59. B. Schweizer, "Statistical metric spaces", Pacific J. Math, 10, pp.314~334 (1960)
  60. M. Sen, "Statistical convergence in intuitionistic fuzzy n-normed Linear Spaces", Fuzzy Inf Eng, 3, pp.259~273 (2011)
  61. M. Sen, "Lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces", Math Comput Modelling, 54, pp.2978~2985 (2011)
  62. A. H. Siddiqi, "2-normed spaces", Aligarh Bull. math., pp.53~70 (1980)
  63. N. Thillaigovindan, "On lacunary statistical convergence in intuitionistic fuzzy n-normed linear spaces", Ann. Fuzzy Math. Inform, 1(2), pp.119~131 (2011)
  64. G. A. Turan, "On new modular sequence space defined over 2-normed spaces", J. BAUN Inst. Sci. Technol, 22(1), pp.248~254 (2020)
  65. N. Turan, "Quasi statistical convergence in cone metric spaces", Facta Univ. (NIS)Ser. Math. Inform, 33(4), pp.613~626 (2018)
  66. Srinivasan Vijayabalaji, "Intuitionistic fuzzy $n$-normed linear space", 대한수학회보, 44(2), pp.291~308 (2007), 대한수학회
  67. A. White Jr. George, "2-Banach spaces", Math. Nachr, 42, pp.43~60 (1969)
  68. L. A. Zadeh, "Fuzzy sets", Inform. Control, 8, pp.338~353 (1965)

관련 논문AI추천

On lacunary $\Delta^{m}$-statistical convergence of triple sequence in intuitionistic fuzzy n-normed spaceAsif Hussain Jan, TANWEER JALAL강원경기수학회 · 한국수학논문집2023 · 제31권 제3호Some results on $\left( \lambda ,\mu \right) $-statistical convergence of sequences in gradual $n$-normed linear spacesMehmet Gurdal, Nagihan Ustunsoy, Omer KISI기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2023 · 제25권 제3호Lacunary Statically Convergent and Lacunary Strongly Convergent Generalized Difference Sequences of Fuzzy Real NumbersAchyutanada Baruah, Binod Chandra Tripathy경북대학교 자연과학대학 수학과 · Kyungpook Mathematical Journal2010 · 제50권 제4호A note on lacunary statistically convergent double sequences of fuzzy numbersYavuz Altin대한수학회 · 대한수학회논문집2008 · 제23권 제2호On paranorm type intuitionistic fuzzy Zweier I-convergent sequence spacesAyhan Esi, Hira Fatima, Vakeel A. Khan, Yasmeen기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제13권 제1호$I_{\lambda}$-convergence in intuitionistic fuzzy $n$-normed linear spaceNabanita Konwar, Pradip Debnath기초자연과학연구소 · ANNALS OF FUZZY MATHEMATICS AND INFORMATICS2017 · 제13권 제1호

이 간행물의 다른 논문 (6건)

Intuitionistic fuzzification of essential submodule with respect to an arbitrary submoduleP. K. Sharmapp. 223-234A note on ideals of the nearness hemiringsM. A. Ozturkpp. 235-242Tripolar fuzzy interior ideals and tripolar fuzzy soft interior ideals over semigroupsMarapureddy Murali Krishna Raopp. 243-256Soft Topological Soft ModulesFawzan Sidky, M. E. El-Shafei, M. K. Tahatpp. 257-272Topological structures based on interval-valued sets김준희, 허걸, 이정곤, 전영배pp. 273-295
원문 보기