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Lacunary I^*-Yakınsaklık ve Lacunary I^*-Cauchy Dizisi

Year 2023, Volume: 23 Issue: 6, 1434 - 1439, 28.12.2023
https://doi.org/10.35414/akufemubid.1332740

Abstract

Yapılan bu çalışmada, öncelikle, lacunary I^*-yakınsaklık kavramı tanımlandı ve lacunary I-yakınsaklık kavramı ile lacunary I^*-yakınsaklık kavramı arasındaki ilişkiler incelendi. Daha sonra, lacunary I^*-Cauchy dizi kavramı tanımladı ve lacunary I-Cauchy dizisi ile lacunary I^*-Cauchy dizisi arasındaki ilişkiler araştırıldı. Ayrıca, çalışmanın sonunda, lacunary I-yakınsaklık kavramı ile I-Cauchy dizisi kavramı arasındaki ilişki ele alındı.

References

  • Das P., Savaş E. and Ghosal S. K., 2011. On generalized of certain summability methods using ideals. Applied Mathematics Letters, 24(9), 1509-1514.
  • Debnath P., 2012. Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces. Computers and Mathematics with Applications, 63(3), 708–715.
  • Dündar E. and Altay B., 2014. I_2-convergence and I_2-Cauchy of double sequences. Acta Mathematica Scientia, 34(2) , 343–353.
  • Dündar E. and Altay B., 2011, On some properties of I_2-convergence and I_2-Cauchy of double sequences. General Mathematics Notes, 7(1), 1–12.
  • Dündar E., Ulusu U. and Pancarog ̆lu N., 2016. Strongly I_2-lacunary convergence and I_2-lacunary Cauchy double sequences of sets. The Aligarh Bulletin of Mathematics, 35(1-2), 1–15.
  • Dündar E. and Ulusu U., 2023. On Rough I-convergence and I-Cauchy sequence for functions defined on amenable semigroup. Universal Journal of Mathematics and Applications, 6(2), 86–90.
  • Fast H., 1951. Sur la convergence statistique. Colloquium Mathematicae, 2(3-4), 241–244.
  • Freedman A. R., Sember J. J. and Raphael M., 1978. Some Cesàro type summability spaces. Proceedings of the London Mathematical Society, 3(3), 508-520.
  • Kostyrko P., Šalát T. and Wilczyński W., 2000. I-convergence, Real Analysis Exchange, 26(2), 669–686.
  • Nabiev A., Pehlivan S. and Gürdal M., 2007. On I-Cauchy sequence. Taiwanese Journal of Mathematics, 11(2), 569–576.
  • Sever Y., Ulusu U. and Dündar E., 2014. On strongly I and I^*-lacunary convergence of sequences of sets. In: AIP Conference Proceedings. American Institute of Physics, 1611(1), 357–362.
  • Schoenberg I. J., 1959. The integrability of certain functions and related summability methods. The American Mathematical Monthly, 66(5), 361–375.
  • Tripathy B. C., Hazarika B. and Choudhary B., 2012. Lacunary I-convergent sequences. Kyungpook Mathematical Journal, 52(4), 473-482.
  • Ulusu U. and Dündar E., 2014. I-lacunary statistical convergence of sequences of sets. Filomat, 28(8), 1567–1574.
  • Ulusu U. and Nuray F., 2020. Lacunary I-invariant convergence. Cumhuriyet Science Journal, 41(3), 617–624. Yamancı U. and Gürdal M. 2013. On lacunary ideal convergence in random-normed space. Journal of Mathematics, 2013, 868457. https://doi.org/10.1155/2013/868457

Lacunary I^*-Convergence and Lacunary I^*-Cauchy Sequence

Year 2023, Volume: 23 Issue: 6, 1434 - 1439, 28.12.2023
https://doi.org/10.35414/akufemubid.1332740

Abstract

In this study conducted, firstly, we defined the concept of lacunary I^*-convergence and we investigated the relations between lacunary I-convergence and lacunary I^*-convergence. Then, we defined the concept of lacunary I^*-Cauchy sequence and investigated the relations between lacunary I-Cauchy sequence and lacunary I^*-Cauchy sequence. Additionally, at the end of the study, we examined the relation between lacunary I^*-convergence and lacunary I-Cauchy sequence.

References

  • Das P., Savaş E. and Ghosal S. K., 2011. On generalized of certain summability methods using ideals. Applied Mathematics Letters, 24(9), 1509-1514.
  • Debnath P., 2012. Lacunary ideal convergence in intuitionistic fuzzy normed linear spaces. Computers and Mathematics with Applications, 63(3), 708–715.
  • Dündar E. and Altay B., 2014. I_2-convergence and I_2-Cauchy of double sequences. Acta Mathematica Scientia, 34(2) , 343–353.
  • Dündar E. and Altay B., 2011, On some properties of I_2-convergence and I_2-Cauchy of double sequences. General Mathematics Notes, 7(1), 1–12.
  • Dündar E., Ulusu U. and Pancarog ̆lu N., 2016. Strongly I_2-lacunary convergence and I_2-lacunary Cauchy double sequences of sets. The Aligarh Bulletin of Mathematics, 35(1-2), 1–15.
  • Dündar E. and Ulusu U., 2023. On Rough I-convergence and I-Cauchy sequence for functions defined on amenable semigroup. Universal Journal of Mathematics and Applications, 6(2), 86–90.
  • Fast H., 1951. Sur la convergence statistique. Colloquium Mathematicae, 2(3-4), 241–244.
  • Freedman A. R., Sember J. J. and Raphael M., 1978. Some Cesàro type summability spaces. Proceedings of the London Mathematical Society, 3(3), 508-520.
  • Kostyrko P., Šalát T. and Wilczyński W., 2000. I-convergence, Real Analysis Exchange, 26(2), 669–686.
  • Nabiev A., Pehlivan S. and Gürdal M., 2007. On I-Cauchy sequence. Taiwanese Journal of Mathematics, 11(2), 569–576.
  • Sever Y., Ulusu U. and Dündar E., 2014. On strongly I and I^*-lacunary convergence of sequences of sets. In: AIP Conference Proceedings. American Institute of Physics, 1611(1), 357–362.
  • Schoenberg I. J., 1959. The integrability of certain functions and related summability methods. The American Mathematical Monthly, 66(5), 361–375.
  • Tripathy B. C., Hazarika B. and Choudhary B., 2012. Lacunary I-convergent sequences. Kyungpook Mathematical Journal, 52(4), 473-482.
  • Ulusu U. and Dündar E., 2014. I-lacunary statistical convergence of sequences of sets. Filomat, 28(8), 1567–1574.
  • Ulusu U. and Nuray F., 2020. Lacunary I-invariant convergence. Cumhuriyet Science Journal, 41(3), 617–624. Yamancı U. and Gürdal M. 2013. On lacunary ideal convergence in random-normed space. Journal of Mathematics, 2013, 868457. https://doi.org/10.1155/2013/868457
There are 15 citations in total.

Details

Primary Language Turkish
Subjects Topology
Journal Section Articles
Authors

Nimet Pancaroğlu Akın 0000-0003-4661-5388

Şeyma Yalvaç 0000-0003-2516-4485

Erdinç Dündar 0000-0002-0545-7486

Early Pub Date December 22, 2023
Publication Date December 28, 2023
Submission Date July 26, 2023
Published in Issue Year 2023 Volume: 23 Issue: 6

Cite

APA Pancaroğlu Akın, N., Yalvaç, Ş., & Dündar, E. (2023). Lacunary I^*-Yakınsaklık ve Lacunary I^*-Cauchy Dizisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, 23(6), 1434-1439. https://doi.org/10.35414/akufemubid.1332740
AMA Pancaroğlu Akın N, Yalvaç Ş, Dündar E. Lacunary I^*-Yakınsaklık ve Lacunary I^*-Cauchy Dizisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. December 2023;23(6):1434-1439. doi:10.35414/akufemubid.1332740
Chicago Pancaroğlu Akın, Nimet, Şeyma Yalvaç, and Erdinç Dündar. “Lacunary I^*-Yakınsaklık Ve Lacunary I^*-Cauchy Dizisi”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 23, no. 6 (December 2023): 1434-39. https://doi.org/10.35414/akufemubid.1332740.
EndNote Pancaroğlu Akın N, Yalvaç Ş, Dündar E (December 1, 2023) Lacunary I^*-Yakınsaklık ve Lacunary I^*-Cauchy Dizisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 23 6 1434–1439.
IEEE N. Pancaroğlu Akın, Ş. Yalvaç, and E. Dündar, “Lacunary I^*-Yakınsaklık ve Lacunary I^*-Cauchy Dizisi”, Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 23, no. 6, pp. 1434–1439, 2023, doi: 10.35414/akufemubid.1332740.
ISNAD Pancaroğlu Akın, Nimet et al. “Lacunary I^*-Yakınsaklık Ve Lacunary I^*-Cauchy Dizisi”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi 23/6 (December 2023), 1434-1439. https://doi.org/10.35414/akufemubid.1332740.
JAMA Pancaroğlu Akın N, Yalvaç Ş, Dündar E. Lacunary I^*-Yakınsaklık ve Lacunary I^*-Cauchy Dizisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2023;23:1434–1439.
MLA Pancaroğlu Akın, Nimet et al. “Lacunary I^*-Yakınsaklık Ve Lacunary I^*-Cauchy Dizisi”. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi, vol. 23, no. 6, 2023, pp. 1434-9, doi:10.35414/akufemubid.1332740.
Vancouver Pancaroğlu Akın N, Yalvaç Ş, Dündar E. Lacunary I^*-Yakınsaklık ve Lacunary I^*-Cauchy Dizisi. Afyon Kocatepe Üniversitesi Fen Ve Mühendislik Bilimleri Dergisi. 2023;23(6):1434-9.