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Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık

Year 2020, Volume: 20 Issue: 2, 207 - 212, 20.05.2020
https://doi.org/10.35414/akufemubid.675886

Abstract

Bu çalışmada, ilk olarak (μ,ν) sezgisel normuna göre I-lacunary istatistiksel yakınsaklık ve kuvvetli I-lacunary yakınsaklık kavramları tanımlandı. Daha sonra bu kavramlar arasındaki ilişkiler incelendi ve bu kavramlar üzerine önemli gözlemler yapıldı. Bununla birlikte, ilgili sezgisel fuzzy normlu uzayda (μ,ν) sezgisel normuna göre I-lacunary istatistiksel yakınsaklık ile I-istatistiksel yakınsaklık arasındaki ilişkiler incelendi.

References

  • Atanassov, K.T., 1986. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87-96.
  • Atanassov, K., Pasi, G. and Yager R., 2002. Intuitionistic fuzzy interpretations of multi-person multicriteria decision making. Proceedings of 2002 First International IEEE Symposium Intelligent Systems, 1 115-119.
  • Bakery, A.A., 2014. Operator ideal of Cesaro type sequence spaces involving Lacunary sequence. Abstract and Applied Analysis, 2014, 6 pp. Article ID 419560.
  • Das, P. and Ghosal, S., 2010. Some further results on I-Cauchy sequences and condition (AP). Computers & Mathematics with Applications, 59, 2597-2600.
  • Das, P, Savaş, E. and Ghosal, SKr., 2011. On generalizations of certain summability methods using ideals. Applied Mathematics Letters, 24, 1509-1514.
  • Debnath P., 2012. Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces. Computers & Mathematics with Applications, 63, 708-715.
  • Debnath P. and Sen M., 2014. Some completeness results in terms of infinite series and quotient spaces in intuitionistic fuzzy n-normed linear spaces. Journal of Intelligent & Fuzzy Systems, 26, 975-782.
  • Debnath P., 2015. Results on lacunary difference ideal convergence in intuitionistic fuzzy normed linear spaces. Journal of Intelligent & Fuzzy Systems, 28, 1299-1306.
  • Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241-244.
  • Fridy, JA., 1985. On statistical convergence. Analysis, 5, 301-313.
  • Fridy, J.A. and Orhan, C., 1993. Lacunary statistical convergence. Pacific Journal of Mathematics, 160(1), 43-51.
  • Fridy, J.A. and Orhan, C., 1993. Lacunary statistical summability. Journal of Mathematical Analysis and Applications, 173, 497-504.
  • Hosseini, S.B., Regan, D.O. and R. Saadati, 2007. Some results of intuitionistic fuzzy spaces. Iranian Journal of Fuzzy Systems, 4(1), 53-64.
  • Karakuş S., Demirci K. and Duman O., 2008. Statistical convergence on intuitionistic fuzzy normed spaces. Chaos, Solitons & Fractals, 35, 763-769.
  • Kostyrko, P., Šalát, T. and Wilczynki, W., 2000. I-convergence. Real Analysis Exchange, 26(2), 669-686.
  • Li, J., 2000. Lacunary statistical convergence and inclusion properties between lacunary methods. International Journal of Mathematics and Mathematical Sciences, 23(3), 175-180.
  • Mursaleen, M. and Mohiuddine, S.A., 2009. On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space. Journal of Computational and Applied Mathematics, 233(2), 142-149.
  • Park, J.H., 2004. Intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals, 22, 1039-1046.
  • Saadati, R. and Park, J.H., 2006. On the intuitionistic fuzzy topological spaces. Chaos, Solitons & Fractals, 27, 331-344. Savaş, E. and Das, P., 2011. A generalized statistical convergence via ideals. Applied Mathematics Letters, 24, 826–30.
  • Savaş E. and Gürdal M., 2015. A generalized statistical convergence in intuitionistic fuzzy normed spaces. Science Asia, 41, 289-294.
  • Šalát, T., 1980. On statistically convergent sequences of real numbers. Mathematica Slovaca, 30, 139-150.
  • Tripathy, B.C., Hazarika, B. and Choudhary, B., 2012. Lacunary I-convergent sequences. Kyungpook Mathematical Journal, 52(4), 473-482.
  • Zadeh, L.A., 1965. Fuzzy sets. Information and Control, 8, 338-353.

I-Lacunary Statistical Convergence in Intuitionistic Fuzzy Normed Spaces

Year 2020, Volume: 20 Issue: 2, 207 - 212, 20.05.2020
https://doi.org/10.35414/akufemubid.675886

Abstract

In this study, first, we investigate the notions of I-lacunary statistical convergence and strongly I-lacunary convergence with regards to the intuitionistic fuzzy norm (IFN for short) (μ,ν). Then, we investigate relationships among this new concepts and make important observations about them. Futhermore, we examine the relations among I-lacunary statistical convergence and I-statistical convergence in terms of IFN (μ,ν) in the corresponding intuitionistic fuzzy normed space.

References

  • Atanassov, K.T., 1986. Intuitionistic fuzzy sets. Fuzzy Sets and Systems, 20, 87-96.
  • Atanassov, K., Pasi, G. and Yager R., 2002. Intuitionistic fuzzy interpretations of multi-person multicriteria decision making. Proceedings of 2002 First International IEEE Symposium Intelligent Systems, 1 115-119.
  • Bakery, A.A., 2014. Operator ideal of Cesaro type sequence spaces involving Lacunary sequence. Abstract and Applied Analysis, 2014, 6 pp. Article ID 419560.
  • Das, P. and Ghosal, S., 2010. Some further results on I-Cauchy sequences and condition (AP). Computers & Mathematics with Applications, 59, 2597-2600.
  • Das, P, Savaş, E. and Ghosal, SKr., 2011. On generalizations of certain summability methods using ideals. Applied Mathematics Letters, 24, 1509-1514.
  • Debnath P., 2012. Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces. Computers & Mathematics with Applications, 63, 708-715.
  • Debnath P. and Sen M., 2014. Some completeness results in terms of infinite series and quotient spaces in intuitionistic fuzzy n-normed linear spaces. Journal of Intelligent & Fuzzy Systems, 26, 975-782.
  • Debnath P., 2015. Results on lacunary difference ideal convergence in intuitionistic fuzzy normed linear spaces. Journal of Intelligent & Fuzzy Systems, 28, 1299-1306.
  • Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicum, 2, 241-244.
  • Fridy, JA., 1985. On statistical convergence. Analysis, 5, 301-313.
  • Fridy, J.A. and Orhan, C., 1993. Lacunary statistical convergence. Pacific Journal of Mathematics, 160(1), 43-51.
  • Fridy, J.A. and Orhan, C., 1993. Lacunary statistical summability. Journal of Mathematical Analysis and Applications, 173, 497-504.
  • Hosseini, S.B., Regan, D.O. and R. Saadati, 2007. Some results of intuitionistic fuzzy spaces. Iranian Journal of Fuzzy Systems, 4(1), 53-64.
  • Karakuş S., Demirci K. and Duman O., 2008. Statistical convergence on intuitionistic fuzzy normed spaces. Chaos, Solitons & Fractals, 35, 763-769.
  • Kostyrko, P., Šalát, T. and Wilczynki, W., 2000. I-convergence. Real Analysis Exchange, 26(2), 669-686.
  • Li, J., 2000. Lacunary statistical convergence and inclusion properties between lacunary methods. International Journal of Mathematics and Mathematical Sciences, 23(3), 175-180.
  • Mursaleen, M. and Mohiuddine, S.A., 2009. On lacunary statistical convergence with respect to the intuitionistic fuzzy normed space. Journal of Computational and Applied Mathematics, 233(2), 142-149.
  • Park, J.H., 2004. Intuitionistic fuzzy metric spaces. Chaos, Solitons & Fractals, 22, 1039-1046.
  • Saadati, R. and Park, J.H., 2006. On the intuitionistic fuzzy topological spaces. Chaos, Solitons & Fractals, 27, 331-344. Savaş, E. and Das, P., 2011. A generalized statistical convergence via ideals. Applied Mathematics Letters, 24, 826–30.
  • Savaş E. and Gürdal M., 2015. A generalized statistical convergence in intuitionistic fuzzy normed spaces. Science Asia, 41, 289-294.
  • Šalát, T., 1980. On statistically convergent sequences of real numbers. Mathematica Slovaca, 30, 139-150.
  • Tripathy, B.C., Hazarika, B. and Choudhary, B., 2012. Lacunary I-convergent sequences. Kyungpook Mathematical Journal, 52(4), 473-482.
  • Zadeh, L.A., 1965. Fuzzy sets. Information and Control, 8, 338-353.
There are 23 citations in total.

Details

Primary Language English
Subjects Engineering
Journal Section Articles
Authors

Ömer Kişi 0000-0001-6844-3092

Publication Date May 20, 2020
Submission Date January 16, 2020
Published in Issue Year 2020 Volume: 20 Issue: 2

Cite

APA Kişi, Ö. (2020). Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 20(2), 207-212. https://doi.org/10.35414/akufemubid.675886
AMA Kişi Ö. Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. May 2020;20(2):207-212. doi:10.35414/akufemubid.675886
Chicago Kişi, Ömer. “Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20, no. 2 (May 2020): 207-12. https://doi.org/10.35414/akufemubid.675886.
EndNote Kişi Ö (May 1, 2020) Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20 2 207–212.
IEEE Ö. Kişi, “Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 20, no. 2, pp. 207–212, 2020, doi: 10.35414/akufemubid.675886.
ISNAD Kişi, Ömer. “Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 20/2 (May 2020), 207-212. https://doi.org/10.35414/akufemubid.675886.
JAMA Kişi Ö. Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2020;20:207–212.
MLA Kişi, Ömer. “Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 20, no. 2, 2020, pp. 207-12, doi:10.35414/akufemubid.675886.
Vancouver Kişi Ö. Sezgisel Fuzzy Normlu Uzaylarda I-Lacunary İstatiksel Yakınsaklık. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2020;20(2):207-12.