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

Year 2023, Volume: 23 Issue: 6, 1434 - 1439, 28.12.2023

Nimet Pancaroğlu Akın , Şeyma Yalvaç , Erdinç Dündar

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.

Keywords

İdeal, Lacunary dizi, I-yakınsaklık, I-Cauchy dizi

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

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.

Keywords

Ideal, Lacunary sequence, I-convergence, 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