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Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence

Yıl 2024, Cilt: 12 Sayı: 1, 20 - 27, 28.01.2024

Nimet Pancaroğlu Akın Erdinç Dündar

https://doi.org/10.36753/mathenot.1330281

Öz

In this paper, we defined the concepts of lacunary $\mathcal{I}^{\ast}$-convergence and strongly lacunary $\mathcal{I}^{\ast}$-convergence. We investigated the relations between strongly lacunary $\mathcal{I}$-convergence and strongly lacunary $\mathcal{I}^{\ast}$-convergence. Also, we defined the concept of strongly lacunary $\mathcal{I}^{\ast}$-Cauchy sequence and investigated the relations between strongly lacunary $\mathcal{I}$-Cauchy sequence and strongly lacunary $\mathcal{I}^{\ast}$-Cauchy sequence.

Anahtar Kelimeler

Ideal Lacunary sequence $\mathcal{I}$-Convergence $\mathcal{I}$-Cauchy Sequence

Kaynakça

  • [1] Fast, H.: Sur la convergence statistique. Colloquium Mathematicum. 2, 241-244 (1951).
  • [2] Schoenberg, I.J.: The integrability of certain functions and related summability methods. The American Mathematical Monthly. 66, 361-375 (1959).
  • [3] Kostyrko, P., Šalát T., Wilczynski,W.: I-convergence. Real Analysis Exchange. 26(2), 669-686 (2000).
  • [4] Nabiev, A., Pehlivan, S., Gürdal, M.: On I-Cauchy sequence. Taiwanese Journal of Mathematics. 11(2), 569-576 (2007).
  • [5] Das, P., SavaŞ, E., Ghosal, S. Kr.: On generalized of certain summability methods using ideals. Applied Mathematics Letters. 36, 1509-1514 (2011).
  • [6] Yamancı, U., Gürdal, M.: On lacunary ideal convergence in random n-normed space, Journal of Mathematics. 2013, Article ID 868457, 8 pages, (2013).
  • [7] Debnath, P.: Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Computers & Mathematics with Applications. 63, 708-715 (2012).
  • [8] Tripathy, B.C., Hazarika, B., Choudhary, B.: Lacunary I-convergent sequences. Kyungpook Mathematical Journal. 52, 473-482 (2012).
  • [9] Nabiev, A., Sava¸s, E., Gürdal, M.: Statistically localized sequences in metric spaces. Journal of Applied Analysis & Computation. 9(2), 739-746 (2019).
  • [10] Şahiner, A., Gürdal. M., Yiğit, T.: Ideal convergence characterization of the completion of linear n-normed spaces. Computers & Mathematics with Applications. 61(3), 683-689 (2011).
  • [11] Savaş, E., Gürdal, M.: I-statistical convergence in probabilistic normed spaces. Bucharest Scientific Bulletin Series A Applied Mathematics and Physics. 77(4), 195-204 (2015).
  • [12] Akın, P. N., Dündar, E., Yalvaç, Ş.: Lacunary I∗-convergence and lacunary I∗-Cauchy sequence. (in review).
  • [13] Dündar, E., Altay, B.: I2-convergence and I2-Cauchy of double sequences. Acta Mathematica Scientia. 34B(2), 343-353 (2014).
  • [14] Dündar, E., Altay B.: On some properties of I2-convergence and I2-Cauchy of double sequences. General Mathematics Notes. 7(1), 1-12 (2011).
  • [15] Dündar, E., Ulusu, U., Pancaroğlu, N.: Strongly I2-lacunary convergence and I2-lacunary Cauchy double sequences of sets. The Aligarh Bulletin Of Mathematics. 35(1-2), 1-5 (2016).
  • [16] Dündar, E., Ulusu, U.: On Rough I-convergence and I-Cauchy sequence for functions defined on amenable semigroup. Universal Journal of Mathematics and Applications. 6(2), 86-90 (2023).
  • [17] Freedman, A. R., Sember, J. J., Raphael, M.: Some Cesàro type summability spaces. Proceedings of the London Mathematical Society. 37, 508-520 (1978).
  • [18] Sever, Y., Ulusu U., Dündar, E.: On strongly I and I∗-lacunary convergence of sequences of sets. AIP Conference Proceedings. 1611(357), 7 pages, (2014).
  • [19] Ulusu, U., Nuray, F.: On strongly lacunary summability of sequences of sets. Journal of Applied Mathematics & Bioinformatics. 3(3), 75-88 (2013).
  • [20] Ulusu, U., Dündar, E: I-lacunary statistical convergence of sequences of sets. Filomat, 28(8), 1567-1574 (2014).
  • [21] Ulusu, U., Nuray, F., Dündar, E.: I-limit and I-cluster points for functions defined on amenable semigroups. Fundamental Journal of Mathematics and Applications. 4(2), 45-48 (2021).

Yıl 2024, Cilt: 12 Sayı: 1, 20 - 27, 28.01.2024

Nimet Pancaroğlu Akın Erdinç Dündar

https://doi.org/10.36753/mathenot.1330281

Öz

Kaynakça

  • [1] Fast, H.: Sur la convergence statistique. Colloquium Mathematicum. 2, 241-244 (1951).
  • [2] Schoenberg, I.J.: The integrability of certain functions and related summability methods. The American Mathematical Monthly. 66, 361-375 (1959).
  • [3] Kostyrko, P., Šalát T., Wilczynski,W.: I-convergence. Real Analysis Exchange. 26(2), 669-686 (2000).
  • [4] Nabiev, A., Pehlivan, S., Gürdal, M.: On I-Cauchy sequence. Taiwanese Journal of Mathematics. 11(2), 569-576 (2007).
  • [5] Das, P., SavaŞ, E., Ghosal, S. Kr.: On generalized of certain summability methods using ideals. Applied Mathematics Letters. 36, 1509-1514 (2011).
  • [6] Yamancı, U., Gürdal, M.: On lacunary ideal convergence in random n-normed space, Journal of Mathematics. 2013, Article ID 868457, 8 pages, (2013).
  • [7] Debnath, P.: Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Computers & Mathematics with Applications. 63, 708-715 (2012).
  • [8] Tripathy, B.C., Hazarika, B., Choudhary, B.: Lacunary I-convergent sequences. Kyungpook Mathematical Journal. 52, 473-482 (2012).
  • [9] Nabiev, A., Sava¸s, E., Gürdal, M.: Statistically localized sequences in metric spaces. Journal of Applied Analysis & Computation. 9(2), 739-746 (2019).
  • [10] Şahiner, A., Gürdal. M., Yiğit, T.: Ideal convergence characterization of the completion of linear n-normed spaces. Computers & Mathematics with Applications. 61(3), 683-689 (2011).
  • [11] Savaş, E., Gürdal, M.: I-statistical convergence in probabilistic normed spaces. Bucharest Scientific Bulletin Series A Applied Mathematics and Physics. 77(4), 195-204 (2015).
  • [12] Akın, P. N., Dündar, E., Yalvaç, Ş.: Lacunary I∗-convergence and lacunary I∗-Cauchy sequence. (in review).
  • [13] Dündar, E., Altay, B.: I2-convergence and I2-Cauchy of double sequences. Acta Mathematica Scientia. 34B(2), 343-353 (2014).
  • [14] Dündar, E., Altay B.: On some properties of I2-convergence and I2-Cauchy of double sequences. General Mathematics Notes. 7(1), 1-12 (2011).
  • [15] Dündar, E., Ulusu, U., Pancaroğlu, N.: Strongly I2-lacunary convergence and I2-lacunary Cauchy double sequences of sets. The Aligarh Bulletin Of Mathematics. 35(1-2), 1-5 (2016).
  • [16] Dündar, E., Ulusu, U.: On Rough I-convergence and I-Cauchy sequence for functions defined on amenable semigroup. Universal Journal of Mathematics and Applications. 6(2), 86-90 (2023).
  • [17] Freedman, A. R., Sember, J. J., Raphael, M.: Some Cesàro type summability spaces. Proceedings of the London Mathematical Society. 37, 508-520 (1978).
  • [18] Sever, Y., Ulusu U., Dündar, E.: On strongly I and I∗-lacunary convergence of sequences of sets. AIP Conference Proceedings. 1611(357), 7 pages, (2014).
  • [19] Ulusu, U., Nuray, F.: On strongly lacunary summability of sequences of sets. Journal of Applied Mathematics & Bioinformatics. 3(3), 75-88 (2013).
  • [20] Ulusu, U., Dündar, E: I-lacunary statistical convergence of sequences of sets. Filomat, 28(8), 1567-1574 (2014).
  • [21] Ulusu, U., Nuray, F., Dündar, E.: I-limit and I-cluster points for functions defined on amenable semigroups. Fundamental Journal of Mathematics and Applications. 4(2), 45-48 (2021).
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Uygulamalı Matematik (Diğer)
Bölüm Articles
Yazarlar

Nimet Pancaroğlu Akın 0000-0003-2886-3679

Erdinç Dündar 0000-0002-0545-7486

Erken Görünüm Tarihi 2 Kasım 2023
Yayımlanma Tarihi 28 Ocak 2024
Gönderilme Tarihi 20 Temmuz 2023
Kabul Tarihi 13 Eylül 2023
Yayımlandığı Sayı Yıl 2024 Cilt: 12 Sayı: 1

Kaynak Göster

APA Pancaroğlu Akın, N., & Dündar, E. (2024). Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence. Mathematical Sciences and Applications E-Notes, 12(1), 20-27. https://doi.org/10.36753/mathenot.1330281
AMA Pancaroğlu Akın N, Dündar E. Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence. Math. Sci. Appl. E-Notes. Ocak 2024;12(1):20-27. doi:10.36753/mathenot.1330281
Chicago Pancaroğlu Akın, Nimet, ve Erdinç Dündar. “Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence”. Mathematical Sciences and Applications E-Notes 12, sy. 1 (Ocak 2024): 20-27. https://doi.org/10.36753/mathenot.1330281.
EndNote Pancaroğlu Akın N, Dündar E (01 Ocak 2024) Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence. Mathematical Sciences and Applications E-Notes 12 1 20–27.
IEEE N. Pancaroğlu Akın ve E. Dündar, “Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence”, Math. Sci. Appl. E-Notes, c. 12, sy. 1, ss. 20–27, 2024, doi: 10.36753/mathenot.1330281.
ISNAD Pancaroğlu Akın, Nimet - Dündar, Erdinç. “Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence”. Mathematical Sciences and Applications E-Notes 12/1 (Ocak 2024), 20-27. https://doi.org/10.36753/mathenot.1330281.
JAMA Pancaroğlu Akın N, Dündar E. Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence. Math. Sci. Appl. E-Notes. 2024;12:20–27.
MLA Pancaroğlu Akın, Nimet ve Erdinç Dündar. “Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence”. Mathematical Sciences and Applications E-Notes, c. 12, sy. 1, 2024, ss. 20-27, doi:10.36753/mathenot.1330281.
Vancouver Pancaroğlu Akın N, Dündar E. Strongly Lacunary $\mathcal{I}^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}^{\ast }$-Cauchy Sequence. Math. Sci. Appl. E-Notes. 2024;12(1):20-7.
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