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Proyecciones (Antofagasta)

Print version ISSN 0716-0917

Proyecciones (Antofagasta) vol.33 no.3 Antofagasta Sept. 2014 

Proyecciones Journal of Mathematics Vol. 33, No 3, pp. 277-285, September 2014. Universidad Católica del Norte Antofagasta - Chile


On /-statistically convergent sequence spaces defined by sequences of Orlicz functions using matrix transformation


Shyamal Debnath

Tripura University

Jayanta Debnath

National Institute of Technology



Recently Savas and Das [12] introduced the notion of I-statistical convergence of sequences of real numbers. In this article we introduced the sequence spaces WI(S) (M, A, p), W01 (S) (M, A, p) and(S) (M, A, p) of real numbers defined by /-statistical convergence using sequences of Orlicz function.We study some basic topological and algebraic properties of these spaces. We investigate some inclusion relations involving these spaces.

Key words : Ideal, /-statistical convergence, Orlicz function, matrix transformation.

AMS (2010) Classification No : 46A45, 40A35, 40C35.


[1] Buck R. C., The measure theoretic approach to density, Amer. J. Math., 68, pp. 560-580, (1946).

[2] Debnath S. and Debnath J., Some generalized statistical convergent sequence spaces of fuzzy numbers via ideals, Math. Sci. Lett., 2, No. 2, pp. 151-154, (2013).

[3] Esi A. and Et M., Some new spaces defined by Orlicz functions, Indian J. Pure and Appl. Math., 31 (8), pp. 967-972, (2000).

[4] Fast H., Sur la convergence statistique, Colloq.Math., pp. 2241-244, (1951).

[5] Fridy J. A., On statistical convergence, Analysis, pp. 301-313, (1985).

[6] Kamthan P. K. and Gupta M., Sequence spaces and series (1980).

[7] Kostyrko P. Salat T., and Wilczynski W., I-convergence, Real analysis exchange, 26 (2), pp. 669-686, (2000/2001).

[8] Lindenstrauss J. and Tzafriri L., On Orlicz sequence spaces, Israel J. Math., 101, pp. 379-390, (1971).

[9] Nakano H., Modular sequence spaces, Proc. Japan Acad., 27, pp. 508512, (1951).

[10] Parashar S.D and Choudhury B., Sequence space defined by orlicz functions, Indian J. Pure and Appl. Math., 25(14), pp. 419-428, (1994).

[11] Salat T., On statistically convergent sequences of real numbers, Math. Slovaka, 30, pp. 139-150, (1980).

[12] Savas E. and Das P., A generalized statistical convergence via ideals, Applied mathematics letters, 24, pp. 826-830, (2011).

[13] Schoenburg I. J., The integrability of certain functions and related summability methods, Am. Math. Mon., 66, pp. 361-375, (1951).

[14] Tripathy B. C. and Chandra P., On some generalized difference para-normed sequence spaces associated with multiplier sequences defined by modulus function, Anal. Theory Appl., 27 (1), pp. 21-27, (2011).

[15] Tripathy B. C. and Dutta H., On some new paranormed difference sequence spaces defined by Orlicz functions, Kyungpook Mathematical Journal, 50 (1), pp. 59-69, (2010).

[16] Tripathy B. C., and Dutta A. J., On I-acceleration convergence of sequences of fuzzy real numbers, Math. Modell. Analysis, 17 (4), pp. 549-557, (2012).

[17] Tripathy B. C. and Hazarika B., Some I-convergent sequence spaces defined by orlicz functions, Acta Math. Appl. Sin., 27(1), pp. 149-154, (2011).

[18] Tripathy B. C. and Hazarika B., Paranorm I-convergent sequence spaces, Math. Slovaka, 59 (4), pp. 485-494, (2009).

[19] Tripathy B. C. and Hazarika B., I-convergent sequence spaces associated with multiplier sequence spaces, Mathematical Inequalities and Applications, 11 (3), pp. 543-548, (2008).

[20] Tripathy B. C. and Hazarika B., I-monotonic and I-convergent sequences, Kyungpook Math. Journal, 51 (2), pp. 233-239, (2011).

[21] Tripathy B. C. and Mahanta S., On I-acceleration convergence of sequences, Journal of the Franklin Institute, 347, pp. 591-598, (2010).

[22] Tripathy B. C. and Sen M., Characterization of some matrix classes involving paranormed sequence spaces,Tamkang Jour. Math., 37(2), pp. 155-162, (2006).

[23] Tripathy B.C., Sen M., and Nath S., I-convergence in probabilistic n-normed space, Soft Comput., 16, pp. 1021-1027, (2012), DOI 10.1007/s00500-011-0799-8.

Shyamal Debnath
Department of Mathematics, Tripura University
e-mail :

Jayanta Debnath
Department of Mathematics
National Institute of Technology
e-mail :

Received : November 2013. Accepted : May 2014