Araştırma Makalesi
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Yıl 2023, Cilt: 6 Sayı: 4, 155 - 161, 18.12.2023

Erdinç Dündar Nimet Pancaroğlu Akın Esra Gülle

https://doi.org/10.32323/ujma.1376849
Cited By: 1

Öz

Kaynakça

  • [1] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [2] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
  • [3] P. Kostyrko, T. Salat, W. Wilczynski, $\mathcal{I}$ -Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [4] A. Nabiev, S. Pehlivan, M. Gürdal, On $\mathcal{I}$ -Cauchy sequence, Taiwanese J. Math., 11(2) (2007), 569–576.
  • [5] U. Yamancı, M. Gürdal, On lacunary ideal convergence in random n-normed space, J. Math., 2013 (2013), Article ID 868457, 8 pages.
  • [6] B. C. Tripathy, B. Hazarika, B. Choudhary, Lacunary $\mathcal{I}$ -convergent sequences, Kyungpook Math. J., 52 (2012), 473–482.
  • [7] N. P. Akın, E. Dündar, S¸ . Yalvaç, Lacunary $\mathcal{I}^{\ast }$ -convergence and lacunary $\mathcal{I}^{\ast }$ -Cauchy sequence, AKU J. Sci. Eng., (in press).
  • [8] N. P. Akın, E. Dündar, Strongly lacunary $\mathcal{I}^{\ast }$ -convergence and strongly lacunary $\mathcal{I}^{\ast }$ -Cauchy sequence, Math. Sci. Appl. E-Notes, (in press).
  • [9] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, $\mathcal{I}$ and $\mathcal{I}^*$ -convergence of double sequences, Math. Slovaca, 58(5) (2008), 605-620.
  • [10] E. Dündar, B. Altay, $\mathcal{I}_2$ -convergence and $\mathcal{I}_2$ -Cauchy of double sequences, Acta Math. Sci., 34B(2) (2014), 343–353.
  • [11] E. Dündar, B. Altay, On some properties of $\mathcal{I}_2$ -convergence and $\mathcal{I}_2$ -Cauchy of double sequences, Gen. Math. Notes, 7(1) (2011) 1–12.
  • [12] B. Hazarika, Lacunary ideal convergence of multiple sequences, J. Egyptian Math. Soc., 24 (2016), 54–59.
  • [13] E. Dündar, U. Ulusu, N. Pancaroğlu, Strongly $\mathcal{I}_2$ -lacunary convergence and $\mathcal{I}_2$ -lacunary Cauchy double sequences of sets, Aligarh Bull. Math., 35(1-2) (2016), 1–15.
  • [14] N. P. Akın, E. Dündar, On lacunary $\mathcal{I}_2^{\ast }$ -convergence and lacunary $\mathcal{I}_2^{\ast }$ -Cauchy sequence, Commun. Adv. Math. Sci., 6(4) (2023), 188–195.
  • [15] P. Das, E. Savaş, S. Kr. Ghosal, On generalized of certain summability methods using ideals, Appl. Math. Letter, 36 (2011), 1509–1514.
  • [16] P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63 (2012), 708–715.
  • [17] E. Dündar, U. Ulusu, On rough $\mathcal{I}$ -convergence and $\mathcal{I}$ -Cauchy sequence for functions defined on amenable semigroup, Univer. J. Math. Appl., 6(2) (2023), 86–90.
  • [18] A. R. Freedman, J. J. Sember, M. Raphael, Some Cesaro type summability spaces, Proc. Lond. Math. Soc., 37 (1978), 508–520.
  • [19] F. Nuray, E. Dündar, U. Ulusu, Wijsman $\mathcal{I}_2$ -convergence of double sequences of closed sets, Pure Appl. Math. Lett., 2 (2014), 35–39.
  • [20] Y. Sever, U. Ulusu, E. Dündar, On strongly $\mathcal{I}$ and $\mathcal{I}*$ -lacunary convergence of sequences of sets, AIP Conf. Proc., 1611 (2014), 357–362.
  • [21] U. Ulusu, F. Nuray, On strongly lacunary summability of sequences of sets, J. Appl. Math. Bioinform. 3(3) (2013), 75–88.

On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence

Yıl 2023, Cilt: 6 Sayı: 4, 155 - 161, 18.12.2023

Erdinç Dündar Nimet Pancaroğlu Akın Esra Gülle

https://doi.org/10.32323/ujma.1376849
Cited By: 1

Öz

In the study conducted here, we have given some new concepts in summability theory. In this sense, firstly, using the lacunary sequence we have given the concept of strongly $\mathcal{I}_{\theta_2}^{\ast}$-convergence and we have examined the relations between $\mathcal{I}_{\theta_2}^{\ast}$-convergence and strongly $\mathcal{I}_{\theta_2}^{\ast}$-convergence and also between strongly $\mathcal{I}_{\theta_2}$-convergence and strongly $\mathcal{I}_{\theta_2}^{\ast}$-convergence. Also, using the lacunary sequence we have given the concept of strongly $\mathcal{I}_{\theta_2}^{\ast}$-Cauchy sequence and examined the relations between strongly $\mathcal{I}_{\theta_2}$-Cauchy sequence and strongly $\mathcal{I}_{\theta_2}^{\ast}$-Cauchy sequence.

Anahtar Kelimeler

$\mathcal{I}_2$-Cauchy Sequence $\mathcal{I}_2$-Convergence Double sequence Ideal Lacunary sequence

Kaynakça

  • [1] I. J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66 (1959), 361–375.
  • [2] H. Fast, Sur la convergence statistique, Colloq. Math., 2 (1951), 241–244.
  • [3] P. Kostyrko, T. Salat, W. Wilczynski, $\mathcal{I}$ -Convergence, Real Anal. Exchange, 26(2) (2000), 669–686.
  • [4] A. Nabiev, S. Pehlivan, M. Gürdal, On $\mathcal{I}$ -Cauchy sequence, Taiwanese J. Math., 11(2) (2007), 569–576.
  • [5] U. Yamancı, M. Gürdal, On lacunary ideal convergence in random n-normed space, J. Math., 2013 (2013), Article ID 868457, 8 pages.
  • [6] B. C. Tripathy, B. Hazarika, B. Choudhary, Lacunary $\mathcal{I}$ -convergent sequences, Kyungpook Math. J., 52 (2012), 473–482.
  • [7] N. P. Akın, E. Dündar, S¸ . Yalvaç, Lacunary $\mathcal{I}^{\ast }$ -convergence and lacunary $\mathcal{I}^{\ast }$ -Cauchy sequence, AKU J. Sci. Eng., (in press).
  • [8] N. P. Akın, E. Dündar, Strongly lacunary $\mathcal{I}^{\ast }$ -convergence and strongly lacunary $\mathcal{I}^{\ast }$ -Cauchy sequence, Math. Sci. Appl. E-Notes, (in press).
  • [9] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, $\mathcal{I}$ and $\mathcal{I}^*$ -convergence of double sequences, Math. Slovaca, 58(5) (2008), 605-620.
  • [10] E. Dündar, B. Altay, $\mathcal{I}_2$ -convergence and $\mathcal{I}_2$ -Cauchy of double sequences, Acta Math. Sci., 34B(2) (2014), 343–353.
  • [11] E. Dündar, B. Altay, On some properties of $\mathcal{I}_2$ -convergence and $\mathcal{I}_2$ -Cauchy of double sequences, Gen. Math. Notes, 7(1) (2011) 1–12.
  • [12] B. Hazarika, Lacunary ideal convergence of multiple sequences, J. Egyptian Math. Soc., 24 (2016), 54–59.
  • [13] E. Dündar, U. Ulusu, N. Pancaroğlu, Strongly $\mathcal{I}_2$ -lacunary convergence and $\mathcal{I}_2$ -lacunary Cauchy double sequences of sets, Aligarh Bull. Math., 35(1-2) (2016), 1–15.
  • [14] N. P. Akın, E. Dündar, On lacunary $\mathcal{I}_2^{\ast }$ -convergence and lacunary $\mathcal{I}_2^{\ast }$ -Cauchy sequence, Commun. Adv. Math. Sci., 6(4) (2023), 188–195.
  • [15] P. Das, E. Savaş, S. Kr. Ghosal, On generalized of certain summability methods using ideals, Appl. Math. Letter, 36 (2011), 1509–1514.
  • [16] P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63 (2012), 708–715.
  • [17] E. Dündar, U. Ulusu, On rough $\mathcal{I}$ -convergence and $\mathcal{I}$ -Cauchy sequence for functions defined on amenable semigroup, Univer. J. Math. Appl., 6(2) (2023), 86–90.
  • [18] A. R. Freedman, J. J. Sember, M. Raphael, Some Cesaro type summability spaces, Proc. Lond. Math. Soc., 37 (1978), 508–520.
  • [19] F. Nuray, E. Dündar, U. Ulusu, Wijsman $\mathcal{I}_2$ -convergence of double sequences of closed sets, Pure Appl. Math. Lett., 2 (2014), 35–39.
  • [20] Y. Sever, U. Ulusu, E. Dündar, On strongly $\mathcal{I}$ and $\mathcal{I}*$ -lacunary convergence of sequences of sets, AIP Conf. Proc., 1611 (2014), 357–362.
  • [21] U. Ulusu, F. Nuray, On strongly lacunary summability of sequences of sets, J. Appl. Math. Bioinform. 3(3) (2013), 75–88.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Erdinç Dündar 0000-0002-0545-7486

Nimet Pancaroğlu Akın 0000-0003-4661-5388

Esra Gülle 0000-0001-5575-2937

Erken Görünüm Tarihi 4 Aralık 2023
Yayımlanma Tarihi 18 Aralık 2023
Gönderilme Tarihi 16 Ekim 2023
Kabul Tarihi 30 Kasım 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 4

Kaynak Göster

APA Dündar, E., Pancaroğlu Akın, N., & Gülle, E. (2023). On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Universal Journal of Mathematics and Applications, 6(4), 155-161. https://doi.org/10.32323/ujma.1376849
AMA Dündar E, Pancaroğlu Akın N, Gülle E. On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Univ. J. Math. Appl. Aralık 2023;6(4):155-161. doi:10.32323/ujma.1376849
Chicago Dündar, Erdinç, Nimet Pancaroğlu Akın, ve Esra Gülle. “On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”. Universal Journal of Mathematics and Applications 6, sy. 4 (Aralık 2023): 155-61. https://doi.org/10.32323/ujma.1376849.
EndNote Dündar E, Pancaroğlu Akın N, Gülle E (01 Aralık 2023) On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Universal Journal of Mathematics and Applications 6 4 155–161.
IEEE E. Dündar, N. Pancaroğlu Akın, ve E. Gülle, “On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”, Univ. J. Math. Appl., c. 6, sy. 4, ss. 155–161, 2023, doi: 10.32323/ujma.1376849.
ISNAD Dündar, Erdinç vd. “On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”. Universal Journal of Mathematics and Applications 6/4 (Aralık 2023), 155-161. https://doi.org/10.32323/ujma.1376849.
JAMA Dündar E, Pancaroğlu Akın N, Gülle E. On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Univ. J. Math. Appl. 2023;6:155–161.
MLA Dündar, Erdinç vd. “On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”. Universal Journal of Mathematics and Applications, c. 6, sy. 4, 2023, ss. 155-61, doi:10.32323/ujma.1376849.
Vancouver Dündar E, Pancaroğlu Akın N, Gülle E. On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Univ. J. Math. Appl. 2023;6(4):155-61.

Cited By

On Strongly Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Strongly Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence
Universal Journal of Mathematics and Applications
https://doi.org/10.32323/ujma.1376849
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Universal Journal of Mathematics and Applications 

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