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Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces

Yıl 2023, Cilt: 11 Sayı: 2, 89 - 96, 30.06.2023

Şeyma Yalvaç Erdinç Dündar

Öz

In this study, firstly, we defined the notions of lacunary invariant convergence and lacunary invariant Cauchy sequence in fuzzy normed spaces. Then, we introduced lacunary strongly invariant convergence in fuzzy normed spaces and we investigated some properties of these new concepts

Anahtar Kelimeler

Fuzzy normed space Invariant convergence Lacunary convergence

Kaynakça

  • [1] Freedman, A.R., Sembrer, J.J., Raphael, M.: Some Cesaro-type summability spaces. Proc. London Math. Soc. 37 3, 508–520 (1978).
  • [2] Bag, T., Samanta, S.K.: Finite dimensional fuzzy normed linear spaces. J. Fuzzy Math. 11 (3) 687–705 (2003).
  • [3] Banach, S.: Théorie des Operations Lineaires. Warszawa (1932).
  • [4] Chang, C.L.: Fuzzy topolojical spaces. J. Math. Anal. Appl. 24, 182–190 (1968).
  • [5] Cheng, S.C., Mordeson, J.N.: Fuzzy linear operator and fuzzy normed linear spaces. Bull. Calcutta Math. Soc. 86, 429–436 (1994).
  • [6] Das, N.R., Das, P.: Fuzzy topology generated by fuzzy norm. Fuzzy Sets and Systems. 107, 349–354 (1999).
  • [7] Das, G., Patel, B.K.: Lacunary distribution of sequences. Indian J. Pure Appl. Math. 20 (1), 64–74 (1989).
  • [8] Dean, D., Raimi, R.A.: Permutations with comparable sets of invariant means. Duke Math. 27, 467–480 (1960).
  • [9] Diamond, P., Kloeden, P.: Metric spaces of fuzzy sets: theory and aplications. World Scientific, Singapore(1994).
  • [10] Fang, J.-X.: A note on the completions of fuzzy metric spaces and fuzzy normed space. Fuzzy Sets and Systems. 131, 399–407 (2002).
  • [11] Fang, J.-X., Huang, H.: On the level convergence of a sequence of fuzzy numbers. Fuzzy Sets and Systems. 147, 417–435 (2004).
  • [12] Felbin, C.: Finite dimensional fuzzy normed linear space. Fuzzy Sets and Systems. 48, 293–248 (1992).
  • [13] George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets and Sytems. 64, 395–399 (1994).
  • [14] Goetschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets and Systems. 18, 31–43 (1986).
  • [15] Itoh, M., Cho, M.: Fuzzy bounded operators. Fuzzy Sets and Systems. 93, 353–362 (1998).
  • [16] Kaleva, O., Seikkala, S.: On fuzzy metric spaces. Fuzzy Sets and Sytems. 12, 215–229 (1984).
  • [17] Katsaras, A.K.: Fuzzy topological vector spaces II. Fuzzy Sets and Systems. 12, 143–154 (1984).
  • [18] Kramosil, I., Michalek, J.: Fuzzy metrics and statistical metric spaces. Kybernetika. 11, 336–344 (1975).
  • [19] Lorentz, G.: A contribution to the theory of divergent sequences. Acta Math. 80, 167–190 (1948).
  • [20] Michalek, J.: Fuzzy topologies. Kybernetika. 11, 345–354 (1975).
  • [21] Mizumoto, M., Tanaka, K.: Some properties of fuzzy numbers. Advances in Fuzzy Set Theory and applications. North-Holland, Amsterdam. 153–164 (1979).
  • [22] Mursaleen, M.: On some new invariant matrix methods of summability. Quart. J. Math. Oxford. 34, 77–86 (1983).
  • [23] Mursaleen, M.: Matrix transformations between some new sequence spaces. Houston J. Math. 9, 505–509 (1983).
  • [24] Mursaleen, M., Edely, O. H. H.: On the invariant mean and statistical convergence. Appl. Math. Lett. 22, 1700–1704 (2009).
  • [25] Raimi, R.A.: Invariant means and invariant matrix methods of summability. Duke Math. J. 30, 81–94 (1963).
  • [26] Savaş, E.: Strong -convergent sequences. Bull. Calcutta Math. 81, 295–300 (1989).
  • [27] Savaş, E.: On lacunary strong -convergence. Indian J. Pure Appl. Math. 21, 359–365 (1990).
  • [28] Schaefer, P.: Infinite matrices and invariant means. Proc. Amer. Math. Soc. 36, 104–110 (1972).
  • [29] Şençimen, C., Pehlivan, S.: Statistical convergence in fuzzy normed linear spaces. Fuzzy Sets and Systems 159, 361–370 (2008).
  • [30] Türkmen, M. R., Cinar, M.: Lacunary statistical convergence in fuzzy normed linear spaces. App. and Comp. Math. 6 (5), 233–237 (2017).
  • [31] Xiao, J., Zhu, X.: On linearly topological structure and property of fuzzy normed linear space. Fuzzy Sets and Systems 125, 153–161 (2002).
  • [32] Yalvaç, Ş., Dündar, E.: Invariant convergence in fuzzy normed spaces. Honam Math. J. 43(3), 433–440 (2021).
  • [33] Zadeh, L. A.: Fuzzy sets. Inform. and Control. 8, 338–353 (1965).

Yıl 2023, Cilt: 11 Sayı: 2, 89 - 96, 30.06.2023

Şeyma Yalvaç Erdinç Dündar

Öz

Kaynakça

  • [1] Freedman, A.R., Sembrer, J.J., Raphael, M.: Some Cesaro-type summability spaces. Proc. London Math. Soc. 37 3, 508–520 (1978).
  • [2] Bag, T., Samanta, S.K.: Finite dimensional fuzzy normed linear spaces. J. Fuzzy Math. 11 (3) 687–705 (2003).
  • [3] Banach, S.: Théorie des Operations Lineaires. Warszawa (1932).
  • [4] Chang, C.L.: Fuzzy topolojical spaces. J. Math. Anal. Appl. 24, 182–190 (1968).
  • [5] Cheng, S.C., Mordeson, J.N.: Fuzzy linear operator and fuzzy normed linear spaces. Bull. Calcutta Math. Soc. 86, 429–436 (1994).
  • [6] Das, N.R., Das, P.: Fuzzy topology generated by fuzzy norm. Fuzzy Sets and Systems. 107, 349–354 (1999).
  • [7] Das, G., Patel, B.K.: Lacunary distribution of sequences. Indian J. Pure Appl. Math. 20 (1), 64–74 (1989).
  • [8] Dean, D., Raimi, R.A.: Permutations with comparable sets of invariant means. Duke Math. 27, 467–480 (1960).
  • [9] Diamond, P., Kloeden, P.: Metric spaces of fuzzy sets: theory and aplications. World Scientific, Singapore(1994).
  • [10] Fang, J.-X.: A note on the completions of fuzzy metric spaces and fuzzy normed space. Fuzzy Sets and Systems. 131, 399–407 (2002).
  • [11] Fang, J.-X., Huang, H.: On the level convergence of a sequence of fuzzy numbers. Fuzzy Sets and Systems. 147, 417–435 (2004).
  • [12] Felbin, C.: Finite dimensional fuzzy normed linear space. Fuzzy Sets and Systems. 48, 293–248 (1992).
  • [13] George, A., Veeramani, P.: On some results in fuzzy metric spaces. Fuzzy Sets and Sytems. 64, 395–399 (1994).
  • [14] Goetschel, R., Voxman, W.: Elementary fuzzy calculus. Fuzzy Sets and Systems. 18, 31–43 (1986).
  • [15] Itoh, M., Cho, M.: Fuzzy bounded operators. Fuzzy Sets and Systems. 93, 353–362 (1998).
  • [16] Kaleva, O., Seikkala, S.: On fuzzy metric spaces. Fuzzy Sets and Sytems. 12, 215–229 (1984).
  • [17] Katsaras, A.K.: Fuzzy topological vector spaces II. Fuzzy Sets and Systems. 12, 143–154 (1984).
  • [18] Kramosil, I., Michalek, J.: Fuzzy metrics and statistical metric spaces. Kybernetika. 11, 336–344 (1975).
  • [19] Lorentz, G.: A contribution to the theory of divergent sequences. Acta Math. 80, 167–190 (1948).
  • [20] Michalek, J.: Fuzzy topologies. Kybernetika. 11, 345–354 (1975).
  • [21] Mizumoto, M., Tanaka, K.: Some properties of fuzzy numbers. Advances in Fuzzy Set Theory and applications. North-Holland, Amsterdam. 153–164 (1979).
  • [22] Mursaleen, M.: On some new invariant matrix methods of summability. Quart. J. Math. Oxford. 34, 77–86 (1983).
  • [23] Mursaleen, M.: Matrix transformations between some new sequence spaces. Houston J. Math. 9, 505–509 (1983).
  • [24] Mursaleen, M., Edely, O. H. H.: On the invariant mean and statistical convergence. Appl. Math. Lett. 22, 1700–1704 (2009).
  • [25] Raimi, R.A.: Invariant means and invariant matrix methods of summability. Duke Math. J. 30, 81–94 (1963).
  • [26] Savaş, E.: Strong -convergent sequences. Bull. Calcutta Math. 81, 295–300 (1989).
  • [27] Savaş, E.: On lacunary strong -convergence. Indian J. Pure Appl. Math. 21, 359–365 (1990).
  • [28] Schaefer, P.: Infinite matrices and invariant means. Proc. Amer. Math. Soc. 36, 104–110 (1972).
  • [29] Şençimen, C., Pehlivan, S.: Statistical convergence in fuzzy normed linear spaces. Fuzzy Sets and Systems 159, 361–370 (2008).
  • [30] Türkmen, M. R., Cinar, M.: Lacunary statistical convergence in fuzzy normed linear spaces. App. and Comp. Math. 6 (5), 233–237 (2017).
  • [31] Xiao, J., Zhu, X.: On linearly topological structure and property of fuzzy normed linear space. Fuzzy Sets and Systems 125, 153–161 (2002).
  • [32] Yalvaç, Ş., Dündar, E.: Invariant convergence in fuzzy normed spaces. Honam Math. J. 43(3), 433–440 (2021).
  • [33] Zadeh, L. A.: Fuzzy sets. Inform. and Control. 8, 338–353 (1965).
Toplam 33 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Matematik
Bölüm Articles
Yazarlar

Şeyma Yalvaç 0000-0003-2516-4485

Erdinç Dündar 0000-0002-0545-7486

Yayımlanma Tarihi 30 Haziran 2023
Gönderilme Tarihi 27 Haziran 2022
Kabul Tarihi 10 Kasım 2022
Yayımlandığı Sayı Yıl 2023 Cilt: 11 Sayı: 2

Kaynak Göster

APA Yalvaç, Ş., & Dündar, E. (2023). Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces. Mathematical Sciences and Applications E-Notes, 11(2), 89-96. https://doi.org/10.36753/mathenot.1136328
AMA Yalvaç Ş, Dündar E. Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces. Math. Sci. Appl. E-Notes. Haziran 2023;11(2):89-96. doi:10.36753/mathenot.1136328
Chicago Yalvaç, Şeyma, ve Erdinç Dündar. “Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces”. Mathematical Sciences and Applications E-Notes 11, sy. 2 (Haziran 2023): 89-96. https://doi.org/10.36753/mathenot.1136328.
EndNote Yalvaç Ş, Dündar E (01 Haziran 2023) Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces. Mathematical Sciences and Applications E-Notes 11 2 89–96.
IEEE Ş. Yalvaç ve E. Dündar, “Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces”, Math. Sci. Appl. E-Notes, c. 11, sy. 2, ss. 89–96, 2023, doi: 10.36753/mathenot.1136328.
ISNAD Yalvaç, Şeyma - Dündar, Erdinç. “Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces”. Mathematical Sciences and Applications E-Notes 11/2 (Haziran 2023), 89-96. https://doi.org/10.36753/mathenot.1136328.
JAMA Yalvaç Ş, Dündar E. Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces. Math. Sci. Appl. E-Notes. 2023;11:89–96.
MLA Yalvaç, Şeyma ve Erdinç Dündar. “Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces”. Mathematical Sciences and Applications E-Notes, c. 11, sy. 2, 2023, ss. 89-96, doi:10.36753/mathenot.1136328.
Vancouver Yalvaç Ş, Dündar E. Lacunary Strongly Invariant Convergence in Fuzzy Normed Spaces. Math. Sci. Appl. E-Notes. 2023;11(2):89-96.
 Kapak Resmi İndir

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