On some I -convergent generalized difference sequence spaces associated with multiplier sequence defined by a sequence of modulli
DOI:
https://doi.org/10.4067/S0716-09172015000200003Keywords:
Ideal, I – convergence, Modulus function, Difference sequence.Abstract
In this article we introduce the sequence spaces cI (F, Λ, ∆m,p), coI (F, Λ, Δm,p) and l∞I (F, Λ, Δm,p), associated with the multiplier sequence Λ = (λk), defined by a sequence of modulli F = (fk). We study some basic topological and algebraic properties of these spaces. Also some inclusion relations are studied.References
[1] A. Esi and M. Et. : Some new spaces defined by Orlicz functions; Indian J. Pure and Appl. Math., 31 (8), pp. 967-972, (2000).
[2] B. C. Tripathy, A. Baruah, M. Et and M. Gungor: On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers, Iranian J. Sci. and Techno., Transactions A: Science, 36 (2), pp. 147-155, (2012).
[3] B. C. Tripathy and A. J. Dutta : On I-acceleration convergence of sequences of fuzzy real numbers; Math. Modell. Analysis, 17 (4), pp. 549-557, (2012).
[4] B. C. Tripathy, B. Choudhury and B. Sarma : On some new type of generalized difference sequence spaces; Kyungpook Math. Jour., 48 (4), pp. 613-622, (2008).
[5] B. C. Tripathy and B. Hazarika : Some I-convergent sequence spaces defined by Orlicz functions; Acta Math. Appl. Sin., 27 (1), pp. 149-154 (2011).
[6] B. C.Tripathy and B.Hazarika : Paranorm I-convergent sequence spaces; Math. Slovaca, 59 (4), pp. 485-494, (2009).
[7] B. C.Tripathy and B. Hazarika : I-convergent sequence spaces associated with multiplier sequence spaces; Math. Ineq. Appl.,11 (3), pp. 543-548, (2008).
[8] B. C. Tripathy and B. Hazarika : I-monotonic and I-convergent sequences; Kyungpook Math. J., 51 (2), pp. 233-239, (2011).
[9] B. C. Tripathy and B. Sarma : On I-convergent double sequences of fuzzy real numbers, Kyungpook Math. J.,52 (2), pp. 189-200, (2012).
[10] B. C. Tripathy and H. Dutta: On some new paranormed difference sequence spaces defined by Orlicz functions; Kyungpook Math. J., 50 (1), pp. 59-69, (2010).
[11] B. C. Tripathy, M. Sen and S. Nath: I-convergent in probabilistic n-normed space; Soft Comput., 16, pp. 1021-1027, (2012).
[12] B. C.Tripathy and P.Chandra: On some generalized difference paranormed sequences spaces associated with multiplier sequence defined by modulus function; Anal. Theory and Appl, 27 (1), pp. 21-27, (2011).
[13] B. C. Tripathy and S. Debnath: On generalized difference sequence spaces of fuzzy numbers, Acta Sinet. Tech., Maringa, 35 (1), pp. 117- 121, (2013).
[14] B. C. Tripathy and S. Mahanta: On a class of vector valued sequences associated with multiplier sequences; Acta Math. Appl. Sinica, 20 (3), pp. 487-494, (2004).
[15] B. C. Tripathy and S. Mahanta: On I-acceleration convergence of sequences; J. Frank. Inst., 347, pp. 591-598, (2010).
[16] B. Sarma: I-convergent sequences of fuzzy real numbers defined by Orlicz function; Mathematical Sciences, 6: 53, doi : 10.1186/2251- 7456-6-53, (2012).
[17] E. Savas and P. Das: A generalized statistical convergence via ideals; Appl. Math. Lett, 24, pp. 826-830, (2011).
[18] G. Goes and S. Goes: Sequences of bounded variation and sequences of fourier coefficients; Math. Zeift., 118, pp. 93-102, (1970).
[19] H. Kizmaz : On certain sequence spaces; Canad. Math. Bull., 24 (2), pp. 169-176, (1981).
[20] H. Nakano : Concave Modulars; J.Math Soc. Japan, 5, pp. 29-49, (1953).
[21] I. J. Schoenburg : The integrability of certain functions and related summability methods; Amer. Math. Month, 66, pp. 361-375, (1951).
[22] J. Lindenstrauss and L. Tzafriri: On Orlicz sequence spaces; Israel J. Math, 101, pp. 379-390, (1971).
[23] P. Kostyrko, T.Salat and W.Wilczynski: I-convergence; Real Anal. Exchange, 26 (2), pp. 669-686, (2000/2001).
[24] R. C Buck: The measure theoretic approach to density; Amer. J. Math., 68, pp. 560-580, (1946).
[25] S. Debnath and J.Debnath: Some ideal convergent sequence spaces of fuzzy real numbers; Palestine J. Math, 3 (1), pp. 27-32, (2014).
[26] S. Debnath and J.Debnath: On I-statistically convergent sequence spaces defined by sequences of Orlicz functions using matrix transformation; Proyecciones J. Math, 33 (3), pp. 277-285, (2014).
[27] T. Salat: On statistically convergent sequences of real numbers; Math. Slovaka, 30, pp. 139-150, (1980).
[28] V. A. Khan and K. Ebadullah : I-convergent difference sequence spaces defined by a sequence of modulli; J. Math. Comput. Sci. 2 (2), pp. 265-273, (2012).
[2] B. C. Tripathy, A. Baruah, M. Et and M. Gungor: On almost statistical convergence of new type of generalized difference sequence of fuzzy numbers, Iranian J. Sci. and Techno., Transactions A: Science, 36 (2), pp. 147-155, (2012).
[3] B. C. Tripathy and A. J. Dutta : On I-acceleration convergence of sequences of fuzzy real numbers; Math. Modell. Analysis, 17 (4), pp. 549-557, (2012).
[4] B. C. Tripathy, B. Choudhury and B. Sarma : On some new type of generalized difference sequence spaces; Kyungpook Math. Jour., 48 (4), pp. 613-622, (2008).
[5] B. C. Tripathy and B. Hazarika : Some I-convergent sequence spaces defined by Orlicz functions; Acta Math. Appl. Sin., 27 (1), pp. 149-154 (2011).
[6] B. C.Tripathy and B.Hazarika : Paranorm I-convergent sequence spaces; Math. Slovaca, 59 (4), pp. 485-494, (2009).
[7] B. C.Tripathy and B. Hazarika : I-convergent sequence spaces associated with multiplier sequence spaces; Math. Ineq. Appl.,11 (3), pp. 543-548, (2008).
[8] B. C. Tripathy and B. Hazarika : I-monotonic and I-convergent sequences; Kyungpook Math. J., 51 (2), pp. 233-239, (2011).
[9] B. C. Tripathy and B. Sarma : On I-convergent double sequences of fuzzy real numbers, Kyungpook Math. J.,52 (2), pp. 189-200, (2012).
[10] B. C. Tripathy and H. Dutta: On some new paranormed difference sequence spaces defined by Orlicz functions; Kyungpook Math. J., 50 (1), pp. 59-69, (2010).
[11] B. C. Tripathy, M. Sen and S. Nath: I-convergent in probabilistic n-normed space; Soft Comput., 16, pp. 1021-1027, (2012).
[12] B. C.Tripathy and P.Chandra: On some generalized difference paranormed sequences spaces associated with multiplier sequence defined by modulus function; Anal. Theory and Appl, 27 (1), pp. 21-27, (2011).
[13] B. C. Tripathy and S. Debnath: On generalized difference sequence spaces of fuzzy numbers, Acta Sinet. Tech., Maringa, 35 (1), pp. 117- 121, (2013).
[14] B. C. Tripathy and S. Mahanta: On a class of vector valued sequences associated with multiplier sequences; Acta Math. Appl. Sinica, 20 (3), pp. 487-494, (2004).
[15] B. C. Tripathy and S. Mahanta: On I-acceleration convergence of sequences; J. Frank. Inst., 347, pp. 591-598, (2010).
[16] B. Sarma: I-convergent sequences of fuzzy real numbers defined by Orlicz function; Mathematical Sciences, 6: 53, doi : 10.1186/2251- 7456-6-53, (2012).
[17] E. Savas and P. Das: A generalized statistical convergence via ideals; Appl. Math. Lett, 24, pp. 826-830, (2011).
[18] G. Goes and S. Goes: Sequences of bounded variation and sequences of fourier coefficients; Math. Zeift., 118, pp. 93-102, (1970).
[19] H. Kizmaz : On certain sequence spaces; Canad. Math. Bull., 24 (2), pp. 169-176, (1981).
[20] H. Nakano : Concave Modulars; J.Math Soc. Japan, 5, pp. 29-49, (1953).
[21] I. J. Schoenburg : The integrability of certain functions and related summability methods; Amer. Math. Month, 66, pp. 361-375, (1951).
[22] J. Lindenstrauss and L. Tzafriri: On Orlicz sequence spaces; Israel J. Math, 101, pp. 379-390, (1971).
[23] P. Kostyrko, T.Salat and W.Wilczynski: I-convergence; Real Anal. Exchange, 26 (2), pp. 669-686, (2000/2001).
[24] R. C Buck: The measure theoretic approach to density; Amer. J. Math., 68, pp. 560-580, (1946).
[25] S. Debnath and J.Debnath: Some ideal convergent sequence spaces of fuzzy real numbers; Palestine J. Math, 3 (1), pp. 27-32, (2014).
[26] S. Debnath and J.Debnath: On I-statistically convergent sequence spaces defined by sequences of Orlicz functions using matrix transformation; Proyecciones J. Math, 33 (3), pp. 277-285, (2014).
[27] T. Salat: On statistically convergent sequences of real numbers; Math. Slovaka, 30, pp. 139-150, (1980).
[28] V. A. Khan and K. Ebadullah : I-convergent difference sequence spaces defined by a sequence of modulli; J. Math. Comput. Sci. 2 (2), pp. 265-273, (2012).
How to Cite
[1]
S. Debnath and S. Saha, “On some I -convergent generalized difference sequence spaces associated with multiplier sequence defined by a sequence of modulli”, Proyecciones (Antofagasta, On line), vol. 34, no. 2, pp. 137-146, 1.
Issue
Section
Artículos
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.