Some new generalized I-convergent difference sequence spaces defined by a sequence of moduli
DOI:
https://doi.org/10.4067/S0716-09172013000200005Keywords:
Ideal, Filter, Sequence of moduli, Difference sequence space, I-convergent sequence space.Abstract
In this article we introduce the sequencespace cI0(F,p, ∆nv) and lI∞ (F,p, ∆nv) for the of sequence of modulii F = (/¾) and given some inclusion relations. These results here proved are analogus to those by M.Aiyub [1](Global Journal of Science Frontier Research Mathematics and Decision Sciences 12(9)(2012),32-36)Downloads
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References
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[2] C. A. Bektas, R. Colak, Generalized difference sequence spaces defined by a sequence of moduli, Soochow. J. Math., 29 (2), pp. 215-220, (2003).
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[15] V. A. Khan, Some new generalized difference sequence spaces defined by a sequence of Moduli, App. Math. J. Chinese. Univ., 26 (11), pp. 104-108, (2006).
[16] V. A. Khan and K. Ebadullah, I-convergent difference sequence spaces defined by a sequence of Moduli. j. Math. Comput. Sci., 2 (2), pp. 265-273, (2012).
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[19] E. Kolk, Inclusion theorems for some sequence spaces defined by a sequence of modulii, Acta Comment. Univ. Tartu., 970, pp. 65-72, (1994).
[20] P. Kostyrko, T.S¸alat and W. Wilczynski, I-Convergence, Real Analysis Exchange., 26, pp. 669-686, (2000).
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[22] H. Nakano, Concave modulars, J.Math Soc. Japan., 5, pp. 29-49, (1953).
[23] K. Raj and S. K. Sharma., Difference sequence spaces defined by sequence of modulus function, Proyecciones Journal of Mathematics., 30, pp. 189-199, (2011).
[24] K. Raj and S. K. Sharma., Some difference sequence spaces in a 2- normed spaces using ideal convergence and Musielak Orlicz function, Far East Journal of Mathematical Sciences, 54(2), pp. 149-161, (2011).
[25] W. H. Ruckle, On perfect Symmetric BK-spaces, Math. Ann., 175, pp. 121-126, (1968).
[26] W. H. Ruckle, Symmetric coordinate space and symmetric bases, Canad, J. Math., 19,pp. 828-838, (1967).
[27] W. H. Ruckle, FK-spaces in which the sequence of coordinate vectors is bounded Canad. J. Math., 25(5), pp. 973-975, (1973).
[28] E. Savas, On some generalized sequence spaces defined by a modulus, Indian J. Pure Appl. Math., 30, pp. 459-464, (1999).
[29] T. S¸alat, On statisticaly convergent sequences of real numbers, Math. Slovaca., 30, pp. 139-150, (1980).
[30] T. S¸alat, B. C. Tripathy and M.Ziman, On some properties of Iconvergence, Tatra Mt. Math.Publ., 28, pp. 279-286, (2004).
[31] B. C. Tripathy, B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(4), pp. 485-494, (2009).
[32] B. C. Tripathy, B. Hazarika, Some I-convergent sequence spaces de- fined by orlicz function, Acta Appl. Math. Sinica, 27 (1), pp. 149-154, (2011).
[2] C. A. Bektas, R. Colak, Generalized difference sequence spaces defined by a sequence of moduli, Soochow. J. Math., 29 (2), pp. 215-220, (2003).
[3] V. K. Bhardwaj and N. Singh, On some sequence spaces defined by a modulus, Indian J. Pure Appl. Math., 30, pp. 809-817, (1999).
[4] R.Colak and M. Et, On some generalized difference sequence spaces and related matrix transformations, Hokkaido Math. J., 26 (3), pp. 483-492, (1997).
[5] K. Demirci, I-limit superior and limit inferior, Math.Commun., 6(, pp. 165-172, (2001).
[6] K. Dems, On I-Cauchy sequences, Real Analysis Exchange., 30, pp. 123-128, (2005).
[7] A. Esi and M.Isik, Some generalized difference sequence spaces, Thai J. Math.,3(2), pp. 241-247, (2005).
[8] M. Et, On some topological properties of generalized difference sequence spaces, Internat J. Math, Math.Soc., 24 (11), pp. 785-791, (2000).
[9] M. Et and A. Esi, On K¨othe-Toeplitz duals of generalized difference sequence spaces, Bull Malysian Math., 31, pp. 275-278, (1980).
[10] H. Fast, Sur Ia convergence statistique, Colloq. Math., 2, pp. 241-244, (1951).
[11] J.A. Fridy, On statistical convergence, Analysis., 5, pp. 301-313, (1985).
[12] J. A. Fridy, Statistical limit points, Proc. Amer. Math. Soc., 11, pp. 1187-1192, (1993).
[13] A. K. Gaur and M. Mursaleen, Difference sequence spaces defined by a sequence of moduli,Demonstratio Math., 31, pp. 275-278, (1998).
[14] V. A. Khan, Some inclusion relations between the difference sequence spaces defined by sequence of moduli, J. Indian. Math. Soc., 73 (1-2), pp. 77-81, (2006).
[15] V. A. Khan, Some new generalized difference sequence spaces defined by a sequence of Moduli, App. Math. J. Chinese. Univ., 26 (11), pp. 104-108, (2006).
[16] V. A. Khan and K. Ebadullah, I-convergent difference sequence spaces defined by a sequence of Moduli. j. Math. Comput. Sci., 2 (2), pp. 265-273, (2012).
[17] H. Kizmaz, On certain sequence spaces, Canadian Math. Bull., 24, pp. 169-176, (1981).
[18] E. Kolk, On strong boundedness and summability with respect to a sequence of moduli, Acta Comment. Univ. Tartu., 960, pp. 41-50, (1993).
[19] E. Kolk, Inclusion theorems for some sequence spaces defined by a sequence of modulii, Acta Comment. Univ. Tartu., 970, pp. 65-72, (1994).
[20] P. Kostyrko, T.S¸alat and W. Wilczynski, I-Convergence, Real Analysis Exchange., 26, pp. 669-686, (2000).
[21] I. J. Maddox, Sequence spaces defined by a modulus, Math. Camb. Phil. Soc., 100, pp. 161-166, (1986).
[22] H. Nakano, Concave modulars, J.Math Soc. Japan., 5, pp. 29-49, (1953).
[23] K. Raj and S. K. Sharma., Difference sequence spaces defined by sequence of modulus function, Proyecciones Journal of Mathematics., 30, pp. 189-199, (2011).
[24] K. Raj and S. K. Sharma., Some difference sequence spaces in a 2- normed spaces using ideal convergence and Musielak Orlicz function, Far East Journal of Mathematical Sciences, 54(2), pp. 149-161, (2011).
[25] W. H. Ruckle, On perfect Symmetric BK-spaces, Math. Ann., 175, pp. 121-126, (1968).
[26] W. H. Ruckle, Symmetric coordinate space and symmetric bases, Canad, J. Math., 19,pp. 828-838, (1967).
[27] W. H. Ruckle, FK-spaces in which the sequence of coordinate vectors is bounded Canad. J. Math., 25(5), pp. 973-975, (1973).
[28] E. Savas, On some generalized sequence spaces defined by a modulus, Indian J. Pure Appl. Math., 30, pp. 459-464, (1999).
[29] T. S¸alat, On statisticaly convergent sequences of real numbers, Math. Slovaca., 30, pp. 139-150, (1980).
[30] T. S¸alat, B. C. Tripathy and M.Ziman, On some properties of Iconvergence, Tatra Mt. Math.Publ., 28, pp. 279-286, (2004).
[31] B. C. Tripathy, B. Hazarika, Paranorm I-convergent sequence spaces, Math. Slovaca, 59(4), pp. 485-494, (2009).
[32] B. C. Tripathy, B. Hazarika, Some I-convergent sequence spaces de- fined by orlicz function, Acta Appl. Math. Sinica, 27 (1), pp. 149-154, (2011).
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How to Cite
[1]
“Some new generalized I-convergent difference sequence spaces defined by a sequence of moduli”, Proyecciones (Antofagasta, On line), vol. 32, no. 2, pp. 159–171, May 2013, doi: 10.4067/S0716-09172013000200005.