Abstract
In this article we introduce multiplier type ideal convergent sequence spaces using Zweier transform and de la Vallee Poussin mean. We study some topological and algebraic properties. Further we prove some inclusion relations related to these new spaces.
Similar content being viewed by others
References
Bhardwaj, V.K., Singh, N.: Some sequence space defined by Orlicz functions. Demonstr. Math. 33(3), 571–582 (2000)
Cakalli, H., Hazarika, B.: Ideal quasi-Cauchy sequences. J. Inequal. Appl. 11. doi:10.1186/1029-242X-2012-234 (2012)
Esi, A., Et, M.: Some new sequence spaces defined by a sequence of Orlicz functions. Indian J. Pure Appl. Math. 31(8), 967–972 (2000)
Esi, A.: Some new sequence spaces defined by Orlicz functions. Bull. Inst. Math. Acad. Sin. 27, 71–76 (1999)
Et, M.: On some new Orlicz sequence spaces. J. Anal. 9, 21–28 (2001)
Hazarika, B., Tamang, K., Singh, B.K.: Zweier ideal convergent sequence spaces defined by Orlicz function. J. Math. Comput. Sci. 8(3), 307–318 (2014)
Hazarika, B., Tamang, K., Singh, B.K.: On paranormed Zweier ideal convergent sequence spaces defined by Orlicz function. J. Egypt. Math. Soc. doi:10.1016/j.joems.2013.08.005 (in press)
Hazarika, B.: On generalized difference ideal convergence in random 2-normed spaces. Filomat 26(6), 1265–1274 (2012)
Khamthan, P.K., Gupta, M.: Sequence Spaces and Series. Marcel Dekker, New York (1980)
Khan, V.A., Ebadullah, K., Esi, A., Khan, N., Shafiq, M.: On paranorm Zweier \(\cal I\)-convergent sequences spaces. Int. J. Anal. 2013, 6 (2013)
Korasnoselkii, M.A., Rutitsky, Y.B.: Convex Function and Orlicz Functions. Groningoen, Netherlands (1961)
Kostyrko, P., Salat, T., Wilczynski, W.: \(\cal I\)-convergence. Real Anal. Exch. 26(2), 669–686 (2000)
L. Leindler, Über die de la Vallée-Pousinsche Summierbarkeit allgenmeiner Othogonalreihen, Acta Math. Acad. Sci. Hungar, 16(1965), 375-387
Lindenstrauss, J., Tzafriri, L.: On Orlicz sequence spaces. Isr. J. Pure Math. 101, 379–390 (1971)
Maddox, I.J.: Elements of Functional Analysis. Cambridge University Press, Cambridge (1970)
Malkowsky, E.: Recent results in the theory of matrix transformation in sequence spaces. Math. Vesnik. 49, 187–196 (1997)
Parashar, S.D., Chaudhary, B.: Sequence spaces defined by Orlicz function. Indian J. Pure Appl. Math. 25, 419–428 (1994)
Ruckle, W.H.: FK spaces in which the sequence of coordinate vector is bounded. Can. J. Math. 25, 973–978 (1973)
Sengonul, M.: On the Zweier sequence space. Demonstr. Math. Vol. 40(1), 181–196 (2007)
Simons, S.: The spaces \(l(p_v)\) and \(m(p_v )\). Proc. Lond. Math. Soc. 15(3), 422–436 (1965)
Tripathy, B.C., Hazarika, B.: Some \({\cal I}\)-convergent sequence space defined by Orlicz functions. Acta Math. Appl. Sin. Engl. Ser. 27, 149–154 (2011)
Tripathy, B.C., Hazarika, B.: Paranorm \({\cal I}\)-convergent sequence spaces. Math. Slovaca 59(4), 485–494 (2009)
Tripathy, B.C., Hazarika, B.: \({\cal I}\)-monotonic and \({\cal I}\)-convergent sequences. Kyungpook Math. J. 51, 233–239 (2011)
Tripathy, B.C., Hazarika, B.: \({\cal I}\)-convergent sequence spaces associated with multiplier sequences. Math. Inequal. Appl. 11(3), 543–548 (2008)
Tripathy, B.C., Altin, Y., Et, M.: Generalized difference sequences space on seminormed spaces defined by Orlicz functions. Math. Slovaca 58(3), 315–324 (2008)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Tamang, K., Hazarika, B. On some ideal convergent multiplier sequence spaces using de la Vallee Poussin mean and Zweier operator. Afr. Mat. 27, 631–643 (2016). https://doi.org/10.1007/s13370-015-0364-1
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s13370-015-0364-1