Statistical Convergence of n-Sequences and eta-Dual of Some Classical Sets of n-Sequences


  • Hemen Dutta
  • B Surender Reddy
  • Iqbal H. Jebril
  • Vijay Kumar



n-sequence, statitistical convergence, completeness, Köthe-Toeplitz dual,


In this paper we introduce the notion of n-sequence and extend the notion of statistical convergence to n-sequences. Further we define the notion of eta-dual as a generalization of Köthe-Toeplitz dual for subsets of n-sequence spaces and compute eta-duals of some classical sets of n-sequences.


H. Dutta, On Köthe-Toeplitz and null duals of some difference sequence spaces defined by Orlicz functions, Eur. J. Pure Appl. Math, 2:4 (2009), 554-563.

Ç.A. Bektaş, M. Et and R. Çolak, Generalized difference sequence spaces and their dual spaces, J. Math. Anal. Appl., 292(2004), 423-432.

P. Chandra and B.C. Tripathy, On generalized Köthe-Toeplitz duals of some sequence spaces, Indian J. Pure Appl. Math., 33(2002), 1301-1306.

H. Fast, Surla convergence statistique, Colloq. Math., 2(1951), 241 - 244.

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

J.A. Fridy, Statistical limit points, Proc. Amer. Math. Soc., 118 (1993), 1187-1192.

H. J. Hamilton, Transformations of multiple sequences, Duke Math. J., 2 (1936), 29-60.

P.K. Kamthan and M. Gupta, Sequence Spaces and Series, Marcel Dekker, New York (1981).

G. Köthe and O. Toeplitz, Linear Raume mit unendlichvielen koordinaten and Ringe unenlicher Matrizen, Jour. reine angew Math., 171 (1934), 193-226.

C.G. Lascarides, A study of certain sequence spaces of Maddox and generalization of a theorem of Iyer, Pacific Jour. Math., 38(2) (1971), 487-500.

I. J. Maddox, Continuous and Köthe-Toeplitz duals of certain sequence spaces, Proc. Camb. Phil. Soc., 65 (1969), 431-435.

F. Moricz, Statistical convergence of multiple sequences, Arch. Math., 81(2003), 82 - 89.

M. Mursaleen, H. H. E. Osama, Statistical convergence of double sequences, J. Math. Anal. Appl., 288(2003), 223 - 231.

A. Pringsheim, Zur Theorie der zweifach unendlichen Zahlenfolgen, Math. Ann., 53(1900), 289 - 321.

G. M. Robinson, Divergent double sequences and series, Trans. Amer. Math. Soc., 28 (1926), 50 -73.

H. Steinhaus, Sur la convergence ordinaire et la convergence asymptotique, Colloq. Math., 2 (1951), 73 -74.

I. J. Schoenberg, The integrability of certain function and related summability methods, Amer. Math. Monthly, 66(1959), 361 - 375. [18]T. Salat, On statistically convergent sequences of real numbers, Math. Slovaca, 30(1980), 139 - 150.

B. Sarma, Studies on Some Vector Valued Sequence Spaces and Köthe-Toeplitz Duals, 2005(Ph.D Thesis).

A. Şahiner, M. Gürdal and F. K. Düden, Triple sequences and their statistical convergence, Selçuk J. Appl. Math., 8(2007), 49-55. [21]B.C. Tripathy, Statistically convergent double sequences, Tamkang J. Math., 34(2003), 231-237.