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Yıl 2023, Cilt: 6 Sayı: 4, 188 - 195, 25.12.2023

Nimet Pancaroğlu Akın Erdinç Dündar

https://doi.org/10.33434/cams.1363596
Cited By: 1

Öz

Kaynakça

  • [1] H. Fast, Sur la convergence statistique, Colloq. Math. 2(1951), 241–244.
  • [2] I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(1959), 361–375.
  • [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] P. Das, E. Savaş, S.Kr. Ghosal, On generalized of certain summability methods using ideals, Appl. Math. Letter, 36(2011), 1509–1514.
  • [6] U. Yamancı, M. Gürdal, On lacunary ideal convergence in random n-normed space, J. Math., Volume 2013, Article ID 868457, 8 pages http://dx.doi.org/10.1155/2013/868457
  • [7] P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63(2012), 708–715.
  • [8] B.C. Tripathy, B. Hazarika, B. Choudhary, Lacunary $\mathcal{I}$-convergent sequences, Kyungpook Math. J. 52(2012), 473–482.
  • [9] N.P. Akın, E. Dündar, Ş. Yalvaç, Lacunary I$\mathcal{I}^{\ast }$-convergence and lacunary $\mathcal{I}^{\ast }$-Cauchy sequence, AKU J. Sci. Eng (in press).
  • [10] 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).
  • [11] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, $\mathcal{I}$ and $\mathcal{I}^{\ast }$-convergence of double sequences, Math. Slovaca, 58(5)(2008), 605–620.
  • [12] E. Dündar, B. Altay, $\mathcal{I}_2$-convergence and $\mathcal{I}_2$-Cauchy of double sequences, Acta Math. Sci., 34B(2)(2014), 343–353.
  • [13] 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.
  • [14] E. Dündar, U. Ulusu, N. Pancaroˇglu, 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.
  • [15] B. Hazarika, Lacunary ideal convergence of multiple sequences, J. Egyptian Math. Soc., 24(2016), 54–59.
  • [16] E. Dündar, U. Ulusu, B. Aydın, $\mathcal{I}_2$-lacunary statistical convergence of double sequences of sets, Konuralp J. Math., 5(1)(2017), 1–10.
  • [17] A.R. Freedman, J.J. Sember, M. Raphael, Some Cesaro type summability spaces, Proc. Lond. Math. Soc. 37(1978), 508–520.
  • [18] Y. Sever, U. Ulusu, E. Dündar, On strongly I$\mathcal{I}$and I$\mathcal{I}^{\ast }$-lacunary convergence of sequences of sets, AIP Conf. Proc., 1611(357)(2014); doi: 10.1063/1.4893860, 7 pages.
  • [19] U. Ulusu, F. Nuray, On strongly lacunary summability of sequences of sets, J. Appl. Math. Inform., 3(3)(2013), 75–88.
  • [20] U. Ulusu, E. Dündar, I-lacunary statistical convergence of sequences of sets, Filomat, 28(8)(2014), 1567–1574.

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

Yıl 2023, Cilt: 6 Sayı: 4, 188 - 195, 25.12.2023

Nimet Pancaroğlu Akın Erdinç Dündar

https://doi.org/10.33434/cams.1363596
Cited By: 1

Öz

In the study conducted here, we have given some new concepts in summability. In this sense, firstly, we have given the concept of lacunary $\mathcal{I}_2^{\ast}$-convergence and we have investigated the relations between lacunary $\mathcal{I}_2$-convergence and lacunary $\mathcal{I}_2^{\ast}$-convergence. Also, we have given the concept of lacunary $\mathcal{I}_2^{\ast}$-Cauchy sequence and investigated the
relations between lacunary $\mathcal{I}_2$-Cauchy sequence and lacunary $\mathcal{I}_2^{\ast}$-Cauchy sequence.

Anahtar Kelimeler

Double sequence Ideal convergence Ideal Cauchy sequence Lacunary sequence

Kaynakça

  • [1] H. Fast, Sur la convergence statistique, Colloq. Math. 2(1951), 241–244.
  • [2] I.J. Schoenberg, The integrability of certain functions and related summability methods, Amer. Math. Monthly, 66(1959), 361–375.
  • [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] P. Das, E. Savaş, S.Kr. Ghosal, On generalized of certain summability methods using ideals, Appl. Math. Letter, 36(2011), 1509–1514.
  • [6] U. Yamancı, M. Gürdal, On lacunary ideal convergence in random n-normed space, J. Math., Volume 2013, Article ID 868457, 8 pages http://dx.doi.org/10.1155/2013/868457
  • [7] P. Debnath, Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces, Comput. Math. Appl., 63(2012), 708–715.
  • [8] B.C. Tripathy, B. Hazarika, B. Choudhary, Lacunary $\mathcal{I}$-convergent sequences, Kyungpook Math. J. 52(2012), 473–482.
  • [9] N.P. Akın, E. Dündar, Ş. Yalvaç, Lacunary I$\mathcal{I}^{\ast }$-convergence and lacunary $\mathcal{I}^{\ast }$-Cauchy sequence, AKU J. Sci. Eng (in press).
  • [10] 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).
  • [11] P. Das, P. Kostyrko, W. Wilczynski, P. Malik, $\mathcal{I}$ and $\mathcal{I}^{\ast }$-convergence of double sequences, Math. Slovaca, 58(5)(2008), 605–620.
  • [12] E. Dündar, B. Altay, $\mathcal{I}_2$-convergence and $\mathcal{I}_2$-Cauchy of double sequences, Acta Math. Sci., 34B(2)(2014), 343–353.
  • [13] 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.
  • [14] E. Dündar, U. Ulusu, N. Pancaroˇglu, 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.
  • [15] B. Hazarika, Lacunary ideal convergence of multiple sequences, J. Egyptian Math. Soc., 24(2016), 54–59.
  • [16] E. Dündar, U. Ulusu, B. Aydın, $\mathcal{I}_2$-lacunary statistical convergence of double sequences of sets, Konuralp J. Math., 5(1)(2017), 1–10.
  • [17] A.R. Freedman, J.J. Sember, M. Raphael, Some Cesaro type summability spaces, Proc. Lond. Math. Soc. 37(1978), 508–520.
  • [18] Y. Sever, U. Ulusu, E. Dündar, On strongly I$\mathcal{I}$and I$\mathcal{I}^{\ast }$-lacunary convergence of sequences of sets, AIP Conf. Proc., 1611(357)(2014); doi: 10.1063/1.4893860, 7 pages.
  • [19] U. Ulusu, F. Nuray, On strongly lacunary summability of sequences of sets, J. Appl. Math. Inform., 3(3)(2013), 75–88.
  • [20] U. Ulusu, E. Dündar, I-lacunary statistical convergence of sequences of sets, Filomat, 28(8)(2014), 1567–1574.
Toplam 20 adet kaynakça vardır.

Ayrıntılar

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

Nimet Pancaroğlu Akın 0000-0003-4661-5388

Erdinç Dündar 0000-0002-0545-7486

Erken Görünüm Tarihi 7 Kasım 2023
Yayımlanma Tarihi 25 Aralık 2023
Gönderilme Tarihi 20 Eylül 2023
Kabul Tarihi 1 Kasım 2023
Yayımlandığı Sayı Yıl 2023 Cilt: 6 Sayı: 4

Kaynak Göster

APA Pancaroğlu Akın, N., & Dündar, E. (2023). On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Communications in Advanced Mathematical Sciences, 6(4), 188-195. https://doi.org/10.33434/cams.1363596
AMA Pancaroğlu Akın N, Dündar E. On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Communications in Advanced Mathematical Sciences. Aralık 2023;6(4):188-195. doi:10.33434/cams.1363596
Chicago Pancaroğlu Akın, Nimet, ve Erdinç Dündar. “On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”. Communications in Advanced Mathematical Sciences 6, sy. 4 (Aralık 2023): 188-95. https://doi.org/10.33434/cams.1363596.
EndNote Pancaroğlu Akın N, Dündar E (01 Aralık 2023) On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Communications in Advanced Mathematical Sciences 6 4 188–195.
IEEE N. Pancaroğlu Akın ve E. Dündar, “On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”, Communications in Advanced Mathematical Sciences, c. 6, sy. 4, ss. 188–195, 2023, doi: 10.33434/cams.1363596.
ISNAD Pancaroğlu Akın, Nimet - Dündar, Erdinç. “On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”. Communications in Advanced Mathematical Sciences 6/4 (Aralık 2023), 188-195. https://doi.org/10.33434/cams.1363596.
JAMA Pancaroğlu Akın N, Dündar E. On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Communications in Advanced Mathematical Sciences. 2023;6:188–195.
MLA Pancaroğlu Akın, Nimet ve Erdinç Dündar. “On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence”. Communications in Advanced Mathematical Sciences, c. 6, sy. 4, 2023, ss. 188-95, doi:10.33434/cams.1363596.
Vancouver Pancaroğlu Akın N, Dündar E. On Lacunary $\mathcal{I}_2^{\ast }$-Convergence and Lacunary $\mathcal{I}_2^{\ast }$-Cauchy Sequence. Communications in Advanced Mathematical Sciences. 2023;6(4):188-95.

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
 Kapak Resmi İndir

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