Logarithmic Ideal Convergence

Yıl 2025, Cilt: 25 Sayı: 1, 89 - 94, 07.02.2025

Ayfer Boztepe Erdinç Dündar

https://doi.org/10.35414/akufemubid.1521702

Öz

In this paper, firstly, the concept of I(H,1)-summability is defined and the relation between the concepts of (H,1)-summability and I(H,1)-summability is given. Then, the concept of logarithmic I-convergence and the concept of logarithmic I-Cauchy sequence are defined and their relations is investigated. Also, the concept of logarithmic I*-convergence is defined and its relation with logarithmic I-convergence is investigated. Finally, the concept of logarithmic I*-Cauchy sequence is defined and its relation with logarithmic I-Cauchy sequence is investigated.

Anahtar Kelimeler

I-convergence, Ideal, Logarithmic convergence, I-Cauchy, Logarithmic I-convergence

Logaritmik İdeal Yakınsaklık

Öz

Yapılan bu çalışmada, öncelikle, I(H,1)-toplanabilirlik kavramı tanımlanmıştır ve (H,1)-toplanabilirlik kavramı ile I(H,1)-toplanabilirlik kavramı arasındaki ilişki verilmiştir. Daha sonra, logaritmik I-yakınsaklık kavramı ve logaritmik I-Cauchy dizi kavramı tanımlanarak aralarındaki ilişki araştırılmıştır. Ayrıca logaritmik I^*-yakınsaklık kavramı tanımlanarak logaritmik I-yakınsaklık ile ilişkisi incelenmiştir. Son olarak logaritmik I^*-Cauchy dizi kavramı tanımlanarak logaritmik I-Cauchy dizi ile arasındaki ilişki araştırılmıştır.

Anahtar Kelimeler

Ideal, I-yakınsaklık, Logaritmik yakınsaklık, I-Cauchy, Logaritmik I-yakınsaklık

Kaynakça

• Alghamdi, M.A., Mursaleen, M. and Alotaibi, A., 2013. Logarithmic density and logaritmic statistical convergence. Advances in Difference Equations, 2013 :227. https://doi.org/10.1186/1687-1847-2013-227 Alotaibi, A. and Mursaleen, M., 2012. A-Statistical summability of Fourier series and Walsh-Fourier series. Applied Mathematics and Information Sciences, 6(3), 535-538.
• Das, P., Savaş, E. and Ghosal, S.K., 2011. On generalized of certain summability methods using ideals. Applied Mathematics Letters, 24(9), 1509-1514. https://doi.org/10.1016/j.aml.2011.03.036
• Edely O. H. H. and Mursaleen M, 2009, On statistical A- summability, Mathematics of Computation Modelling, 49, 672-680. https://doi.org/10.1016/j.mcm.2008.05.053
• Fast, H., 1951. Sur la convergence statistique. Colloquium Mathematicae, 2(3-4), 241–244. https://doi.org/10.4064/cm-2-3-4-241-244
• Fridy J. A., 1985. On statistical convergence. Analysis, 5, 301-313. https://doi.org/10.1524/anly.1985.5.4.301 Gürdal, M. and Huban, M. B., 2014. On I-convergence of double sequences in the topology induced by random 2-norms, Matematički Vesnik, 66(1) 73–83.
• Gürdal, M. and Açık, I., 2008. On I-Cauchy sequences in 2-normed spaces, Mathematical Inequalities and Applications, 11(2), 349–354. http://dx.doi.org/10.7153/mia-11-26
• Gürdal, M., Şahiner, A. and Açık, I., 2009. Approximation theory in 2-Banach spaces, Nonlinear Analysis, 71(5-6), 1654–1661. http://dx.doi.org/10.1016/j.na.2009.01.030
• Kostyrko, P., Šalát, T. and Wilczyński, W., 2000. I-convergence, Real Analysis Exchange, 26(2), 669–686. http://dx.doi.org/10.2307/44154069
• Móricz, F., 2004. Theorems relating to statistical harmonic summability and ordinary convergence of slowly decreasing or oscillating sequences, Analysis, 24, 127-145. http://dx.doi.org/10.1524/anly.2004.24.14.127
• Mursaleen, M. and Mohiuddine, S.A., 2012. On ideal convergence in probabilistic normed spaces. Mathematica Slovaca, 62, 49-62. http://dx.doi.org/10.2478/s12175-011-0071-9 Nabiev, A., Pehlivan, S. and Gürdal, M., 2007. On I-Cauchy sequence. Taiwanese Journal of Mathematics, 11(2), 569–576. http://dx.doi.org/10.11650/twjm/1500404709
• Nabiev, A., Savaş, E. and Gürdal, M., 2019. Statistically localized sequences in metric spaces, Journal of Applied Analysis and Computation, 9(2), 739–746. http://dx.doi.org/10.11948/2156-907X.20180157
• Nuray, F., 2022. Lacunary statistical harmonic summability. Journal of Applied Analysis and Computation, 12(1), 294-301. http://dx.doi.org/10.11948/20210155
• Schoenberg, I.J., 1959. The integrability of certain functions and related summability methods. The American Mathematical Monthly, 66(5), 361–375. https://doi.org/10.1080/00029890.1959.11989303
• Şahiner, A., Gürdal, M. and Yigit, T., 2011. Ideal convergence characterization of the completion of linear n-normed spaces. Computers & Mathematics with Applications, 61(3), 683–689. http://dx.doi.org/10.1016/j.camwa.2010.12.015
• Savaş, E. and Gürdal, M., 2015. I-statistical convergence in probabilistic normed spaces. Politehnica University of Bucharest. Scientic Bulletin. Series A. Applied Mathematics and Physics, 77(4), 195–204. Tripathy, B.C., Hazarika, B. and Choudhary, B., 2012. Lacunary I-convergent sequences. Kyungpook Mathematical Journal, 52(4), 473-482. http://dx.doi.org/10.5666/KMJ.2012.52.4.473 Ulusu, U. and Dündar, E., 2014. I-lacunary statistical convergence of sequences of sets. Filomat, 28(8), 1567–1574. http://dx.doi.org/10.2298/FIL1408567U
• Ulusu, U. and Nuray, F., 2020. Lacunary I-invariant convergence. Cumhuriyet Science Journal, 41(3), 617–624. http://dx.doi.org/10.17776/csj.689877
• Yamancı, U. and Gürdal, M. 2013. On lacunary ideal convergence in random-normed space. Journal of Mathematics, 2013, 8 pages. http://dx.doi.org/10.1155/2013/868457