New notions of triple sequences on ideal spaces in metric spaces

Yıl 2021, , 362 - 367, 30.09.2021

Carlos Granados

https://doi.org/10.31197/atnaa.846717

Cited By: 3

Öz

In this paper, the concepts of $ I_{3} $-localized and $ I_{3}^{*} $-localized sequences in metric spaces are introduced. Furthermore, some properties related to the $ I_{3} $-localized and $ I_{3} $-Cauchy sequences are proved. Otherwise, the notions of uniformly $ I_{3} $-localized sequences in metric spaces are defined.

Anahtar Kelimeler

$ I_{3} $-localized sequences, $ I_{3}^{*} $-localized sequence, $ I_{3} $-Cauchy sequences, uniformly $ I_{3} $-localized sequences

Kaynakça

• [1] P. Das, P. Kostyrko, W. Wilczy«ski and P. Malik, I and I ∗ -convergence of double sequences, Mathematica Slovaca 58(2008), no. 5, 605-620.
• [2] P. Kostyrko, T. Salát and W. Wilczy«ski, I-convergence, Real Anal. Exchange 26(2000/2001), 669-686.
• [3] P. Kostyrko, M. Macaj, T. Salát and M. Sleziak, I-Convergence and Extremal I-Limit Points, Math. Slovaca 55 (2005), 443-464.
• [4] L.N. Krivonosov, Localized sequences in metric spaces, Izv. Vyssh. Uchebn. Zaved Mat. 4 (1974), 45-54.
• [5] A.A. Nabiev, E. Savas and M. Gurdal, I-localized sequences in metric spaces, Facta Universitatis 35 (2020), no. 2, 459-469.
• [6] S. Saha, A. Esi and S. Roy, Some new classes of multiplier ideal convergent triple sequences spaces of fuzzy numbers defined by Orlicz functions, Palestine Journal of Mathematics 9 (2020), no. 1, 174-186.
• [7] A. Sahiner and B.C. Tripathy, Some I-related properties of triple sequences, Selcuk J. Appl. Math. 9 (2008), no. 2, 9-18.
• [8] N. Subramanian and A. Esi, On rough convergence variables of triple sequences, Analysis 40(2020), no. 2, 85-88.
• [9] N. Subramanian, A. Esi and A. Esi , Rough I-convergence on triple Bernstein operator sequences, Southeast Asian Bulletin of Mathematics 44(2020), no. 3, 417-432.
• [10] B. Tripathy and B. C. Tripathy, On I-convergent double sequences, Soochow Journal of Mathematics 31 (2005), no. 4, 549-560.
• [11] B.C. Tripathy and S. Mahanta, On I-acceleration convergence of sequences, Journal of the Franklin Institute, 347(2010), 591-598.
• [12] B.C. Tripathy and B. Hazarika, I-convergent sequence spaces associated with multiplier sequence spaces, Math. Ineq. Appl., 11(2008), no. 3, 543-548.
• [13] B.C. Tripathy and M. Sen, On fuzzy I-convergent difference sequence space, Journal of Intelligent and Fuzzy Systems, 25(2013), no. 3, 643-647.
• [14] B.C. Tripathy and M. Sen, Paranormed I-convergent double sequence spaces associated with multiplier sequences, Kyung- pook Math. Journal, 54(2014), no. 2, 321-332.
• [15] B.C. Tripathy and R. Goswami, Multiple sequences in probabilistic normed spaces, Afrika Matematika, 26(2015), no. (5-6), 753-760.
• [16] B.C. Tripathy and R. Goswami, Fuzzy real valued p-absolutely summable multiple sequences in probabilistic normed spaces, Afrika Matematika, 26(2015), (7-8), 1281-1289.