Some vector-valued statistical convergent sequence spaces
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DOI:
https://doi.org/10.26637/mjm302/004Abstract
In the present paper we introduce some vector-valued statistical convergent sequence spaces defined by a sequence of modulus functions associated with multiplier sequences and we also make an effort to study some topological properties and inclusion relation between these spaces.
Keywords:
Modulus function, paranorm space, difference sequence space, statistical convergenceMathematics Subject Classification:
40A05, 46A45, 40C05- Pages: 161-167
- Date Published: 01-04-2015
- Vol. 3 No. 02 (2015): Malaya Journal of Matematik (MJM)
Altinok H., Altin Y., Isik M. The Sequence Space $B v_sigma(M, P, Q, S)$ On Seminormed Spaces, Indian J. Pure Appl. Math., 39 (2008), 49-58.
Colak R. On invariant sequence spaces, Erc. Univ. J. Sci., 5 (1989), 881-887.
Colak R. On certain sequence spaces and their Kothe-Toeplitz duals, Rend. Mat. Appl., Ser, 13 (1993), 27-39.
Et M., Colak R. On some generalized difference sequence spaces, Soochow J. Math., 21 (1995), $377-386$.
Connor J. S. A topological and functional analytic approach to statistical convergence, Appl. Numer. Harmonic Anal.,(1999), 403-413. DOI: https://doi.org/10.1007/978-1-4612-2236-1_23
Fast H. Sur la convergence statistique, Colloq. Math., 2 (1951), 241-244. DOI: https://doi.org/10.4064/cm-2-3-4-241-244
Fridy J. A. On the statistical convergence, Analysis, 5 (1985), 301-303. DOI: https://doi.org/10.1524/anly.1985.5.4.301
Goes G., Goes S. Sequence of bounded variation and sequences of Fourier coefficients, Math. Zeit, 118 (1970), $93-102$. DOI: https://doi.org/10.1007/BF01110177
Gupta M. The generalized spaces $l^1(X)$ and $m_0(X)$, J. Math. Anal. Appl., 76 (1980), 357-366. DOI: https://doi.org/10.1016/0022-247X(80)90153-5
Isik M. On statistical convergence of generalized difference sequence spaces, Soochow J. Math., 30 (2004), $197-$ 205.
Kamthan P. K. Bases in a certain class of Frechet spaces, Tamkang J. Math., 7 (1976), 41-49.
Kizmaz H. On certain sequence spaces, Cand. Math. Bull., 24 (1981), 169-176. DOI: https://doi.org/10.4153/CMB-1981-027-5
Kolk E. The statistical convergence in Banach spaces, Acta. Comment. Univ. Tartu, 928 (1991), 41-52.
Leonard I. E. Banach sequence spaces, J. Math. Anal. Appl., 54 (1976), 245-265. DOI: https://doi.org/10.1016/0022-247X(76)90248-1
Maddox I. J. Statistical convergence in a locally convex space, Math. Proc. Cambridge Phil. Soc., 104 (1988), 141-145. DOI: https://doi.org/10.1017/S0305004100065312
Mursaleen M. A-statistical convergence, Math. Slovaca, 50 (2000), 111-115.
Ratha A., Srivastava P. D. On some vector valued sequence spaces $mathcal{L}_{infty}^{(p)}left(E_k, Lambdaright)$, Ganita, 47 (1996), 1-12.
Raj K., Sharma S. K. Difference sequence spaces defined by sequence of modulus function, Proyecciones, 30 (2011), 189-199.
Raj K., Sharma S. K. Some difference sequence spaces defined by sequence of modulus function, Int. J. Math. Archive, 2 (2011), pp. 236-240. DOI: https://doi.org/10.4067/S0716-09172011000200005
Salat T. On statictical convergent sequences of real numbers, Math. Slovaca, 30 (1980), 139-150.
Savas E. Strong almost convergence and almost $lambda$-statistical convergence, Hokkaido Math. J., 29 (2000), 531566. DOI: https://doi.org/10.14492/hokmj/1350912989
Savas E. On some generalized sequence spaces defined by a modulus, Indian J. pure Appl. Math., 30 (1999), $459-464$.
Schoenberg I. J. The integrability of certain functions and related summability methods, Amer. Math. Monthly, $66(1959), 361-375$ DOI: https://doi.org/10.2307/2308747
Srivastava J. K., Srivastava B. K. Generalized sequence space $c_0(X, lambda, p)$, Indian J. pure Appl. Math., 27 (1996), 73-84.
Tripathy B. C., Sen M. On generalized statistically convergent sequences, Indian J. Pure Appl. Math., 32 (2001), 1689-1694.
Tripathy B. C., Sen M. Vector valued paranormed bounded and null sequence spaces associated with multiplier sequences, Soochow J. Math., 29 (2003), 379-391.
Tripathy B. C., Mahanta S. On a class of vector valued sequences associated with multiplier sequences, Acta Math. Appl. Sinica, 20 (2004), 487-494. DOI: https://doi.org/10.1007/s10255-004-0186-7
Wilansky A. Summability through Functional Analysis, North- Holland Math. Stud. (1984).
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