Abstract
In this paper, we introduce new triple n-normed sequence spaces and establish some of their topological and algebraic properties.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Alotaibi, A., Mursaleen M., Sharma, S.K.: Double sequence spaces over \(n-\)normed spaces defined by a sequence of orlicz functions. J. Ineq. Appl. 2014, 216 (2014)
Debnath, S., Sarma, B., Das, B.C.: Some generalized triple sequence spaces of real numbers. J. Non. Anal. Opt. 6, 71–79 (2015)
Debnath, S., Subramanian, N.: Generalized rough lacunary statistical triple difference sequence spaces in probability of fractional order defined by musielak-orlicz function. Bol. Soc. Paran. Mat. (3s) 37(1), 55–62 (2019)
Esi, A.: On some triple almost lacunary sequence spaces defined by orlicz functions. Res. Rev.: Discret. Math. Struct. 1, 16–25 (2014)
Esi, A., Catalbas, M.N.: Almost convergence of triple sequences G. J. Math. Anal. 2, 6–10 (2014)
Esi, A., Savas, E.: On lacunary statically convergent triple sequences in probabilistic normed space. Appl. Math. Inf. Sci. 9, 2529–2534 (2015)
Fast, H.: Surla convergence statistique. Colloq. Math. 2, 241–244 (1951)
Fridy, J.A.: On statistical convergence. Analysis 5, 301–313 (1985)
Fridy, J.A.: Statistical limit points. Proc. Am. Math. Soc. 11, 1187–1192 (1993)
Gähler, S.: Linear 2-normietre Rume. Math. Nachr. 28, 1–43 (1965)
Jalal, T.: Some new \(I-\)convergent sequence spaces defined by using a sequence of modulus functions in n-normed spaces. Int. J. Math. Arch. 5(9), 202–209 (2014)
Jalal, T.: Some new \(I-\)lacunary generalized difference sequence spaces defined in n-normed spaces. Springer Proc. Math. Sat. 171, 249–258 (2016)
Jalal, T.: Some new lacunary sequence spaces of invariant means defined by musielak-Orlicz functions on \(n\)-normed space. Int. J. P. Appl. Math. 119(7), 1–11 (2018)
Jalal, T., Malik, I.A.: Some new triple sequence spaces over \(n-\)normed space. Proyecciones J. Math. 37(3), 547–564 (2018)
Jalal, T., Malik, I.A.: \(I\)-convergent triple sequence spaces over \(n-\)normed space. Asia Pac. J. Math. 5(2), 233–242 (2018)
Jalal, T., Malik, I.A.: \(I\)-convergence triple difference sequence spaces over \(n-\)normed space. Tbil. Math. J. 11(4), 93–102 (2018)
Kostyrko, P., Salat, T., Wilczynski, W.: \(I-\)convergence. Real Anal. Exch. 26(2), 669–686 (2000)
Kumar, V.: On \(I-\)convergence of double sequences. Math. Commun. 12, 171–181 (2007)
Lindenstrauss, J., Tzafriri, L.: On orlicz sequence spaces. Israel J. Math. 10, 379–390 (1971)
Misiak, A.: \(n-\)Inner product spaces. Math. Nachr. 140, 299–319 (1989)
Mursaleen, M., Edely, O.H.H.: Statistical convergence of double sequences. J. Math. Anal. Appl. 288, 223–231 (2003)
Mursaleen, M., Raj, K., Sharma, S.K.: Some spaces of differences and lacunary statistical convergence in \(n-\)normed space defined by sequence of orlicz functions. Miskolc Math. Notes 16(1), 283–304 (2015)
Salat, T., Tripathy , B.C., Ziman, M.: On some properties of \(I-\)convergence. Tatra Mountain Mathematical Publications, pp. 669–686 (2000)
Sahiner, A., Gurdal, M., Duden, F.K.: Triple Sequences and their statistical convergence. Selcuk J. Appl. Math. 8, 49–55 (2007)
Sahiner, A., Tripathy, B.C.: Some \(I\) related properties of triple sequences. Selcuk J. Appl. Math. 9, 9–18 (2008)
Sharma, S.K., Esi, A.: Some \(I-\)convergent sequence spaces defined by using sequence of moduli and \(n\)–normed space. J. Egyp. Math. Soc. 21(2), 103–107 (2013)
Tripathy, B.C.: Statistically convergent double sequence. Tamkang. J. Math. 34(3), 231–237 (2003)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Singapore Pte Ltd.
About this paper
Cite this paper
Jalal, T., Malik, I.A. (2021). Topological and Algebraic Properties of Triple n-normed Spaces. In: Giri, D., Ho, A.T.S., Ponnusamy, S., Lo, NW. (eds) Proceedings of the Fifth International Conference on Mathematics and Computing. Advances in Intelligent Systems and Computing, vol 1170. Springer, Singapore. https://doi.org/10.1007/978-981-15-5411-7_14
Download citation
DOI: https://doi.org/10.1007/978-981-15-5411-7_14
Published:
Publisher Name: Springer, Singapore
Print ISBN: 978-981-15-5410-0
Online ISBN: 978-981-15-5411-7
eBook Packages: Intelligent Technologies and RoboticsIntelligent Technologies and Robotics (R0)