A study of Nörlund ideal convergent sequence spaces
DOI:
https://doi.org/10.2298/YJOR200716044KKeywords:
Nörlund matrix, matrix transformation, Nörlund I-convergence, Nörlund I-Cauchy, Nörlund I-boundedAbstract
The Nörlund matrix Nt in the theory of sequence space was firstly used by Wang. In this paper, by using the Nörlund mean Nt and the notion of ideal convergence, we introduce some new sequence spaces cI 0(Nt), cI (Nt), and lI∞(Nt) as a domain of Nörlund mean. We study some topological and algebraic properties on these spaces. Further, some inclusion concerning these spaces are discussed.References
Hardy, G.H., “Divergent series”, American Mathematical Society, 334 (2000) 1–400.
Mears, F.M., “The inverse norlund mean”, Annals of Mathematics, 44 (3) (1943) 401–410.
Tripathy, B.C., and Baruah, A., “Nörlund and riesz mean of sequences of fuzzy real numbers”, Applied Mathematics Letters, 23 (5) (2010) 651–655.
Tripathy, B.C., and Dowari, P.J., “Nörlund and riesz mean of sequence of complex uncertain variables”, Filomat, 32 (8) (2018) 2875–2881.
Wang, C.S., “On nörlund sequence spaces”, Tamkang J. Math, 9 (1) (1978) 269–274.
Tug, O., and Basar, F., “On the spaces of norlund null and norlund convergent sequences”, Twms Journal Of Pure And Applied Mathematics, 7 (1) (2016) 76–87.
Kostyrko, P., Macaj, M., and Salat, T., “Statistical convergence and I–convergence”, Real Analysis Exchange, 26 (2) (2000) 669–686.
Šalát, T., Tripathy, B.C., and Ziman, M., “On some properties of I–convergence”, Tatra Mt. Math. Publ, 28 (2) (204) 274–286.
Tripathy, B.C., and Hazarika, B., “I–convergent sequence spaces associated with multiplier sequences”, Mathematical Inequalities and Applications, 11 (3) (2008) 543–548.
Kolk, E., “Matrix transformations related to I-convergent sequences”, Acta et Commentationes Universitatis Tartuensis de Mathematica, 22 (2) (2018) 191–200.
Savaš, E., “On lacunary p-summable convergence of weight g for fuzzy numbers via ideal”, Journal of Intelligent & Fuzzy Systems, 34 (4) (2018) 2121–2127.
Khan, V.A., Rababah, R.K.A., Alshlool, K., Abdullah, S.A., and Ahmad, A., “On ideal convergence fibonacci difference sequence spaces”, Advances in Difference Equations, (1) (2018) 199.
Khan, V.A., Makharesh, A., Alshlool, K., Abdullah, S.A., and Fatima, H., “On fuzzy valued lacunary ideal convergent sequence spaces defined by a compact operator”, Journal of Intelligent & Fuzzy Systems, 35 (4) (2018) 4849-4855.
Filipów, R., Mrożek, N., Reclaw, I., and Szuca, P., “Ideal convergence of bounded sequences”, The Journal of Symbolic Logic, 72 (2) (2007) 501–512.
Khan, V.A., Alshlool, K., and Abdullah, S.A., “Spaces of ideal convergent sequences of bounded linear operators”, Numerical Functional Analysis and Optimization, 39 (12) (2018) 1278–1290.
Khan, V.A., and Khan, N., “On Zweier I-convergent double sequence spaces”, Filomat, 30 (12) (2016) 3361–3369.
Khan, V.A., Rababah, R.K.A., Esi, A., Abdullah, S.A., and Alshlool, K., “Some new spaces of ideal convergent double sequences by using compact operator”, Journal of Applied Sciences, 17 (9) (2017) 467–474.
Tripathy, B.C., Hazarika, B., and Choudhary, B., “Lacunary I-Convergent Sequences”, Kyungpook Mathematical Journal, 52 (4) (2012) 473–482.
Khan, V.A., and Tabassum, S., “On Ideal Convergent Difference Double Sequence Spaces in n-Normed Spaces Defined by Orlicz Function”, Theory and Applications of Mathematics & Computer Science, 3 (1) (2013) 90–98.
Šalát, T., Tripathy, B.C., and Ziman, M., “On I–convergence field”, Ital. J. Pure Appl. Math, 17 (5) (2005) 1–8.
Downloads
Published
Issue
Section
License
Copyright (c) 2021 YUJOR
This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.
