Keywords: convergence; $\mu $-statistical convergence; convergence in $\mu $-density; condition (APO$_{2}$); 2-norm; 2-normed space; paranorm; paranormed space; Orlicz function; sequence space
@article{10_1007_s10587_011_0029_7,
author = {Das, Pratulananda and Savas, Ekrem and Bhunia, Santanu},
title = {Two valued measure and some new double sequence spaces in $2$-normed spaces},
journal = {Czechoslovak Mathematical Journal},
pages = {809--825},
year = {2011},
volume = {61},
number = {3},
doi = {10.1007/s10587-011-0029-7},
mrnumber = {2853094},
zbl = {1249.46003},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0029-7/}
}
TY - JOUR AU - Das, Pratulananda AU - Savas, Ekrem AU - Bhunia, Santanu TI - Two valued measure and some new double sequence spaces in $2$-normed spaces JO - Czechoslovak Mathematical Journal PY - 2011 SP - 809 EP - 825 VL - 61 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0029-7/ DO - 10.1007/s10587-011-0029-7 LA - en ID - 10_1007_s10587_011_0029_7 ER -
%0 Journal Article %A Das, Pratulananda %A Savas, Ekrem %A Bhunia, Santanu %T Two valued measure and some new double sequence spaces in $2$-normed spaces %J Czechoslovak Mathematical Journal %D 2011 %P 809-825 %V 61 %N 3 %U http://geodesic.mathdoc.fr/articles/10.1007/s10587-011-0029-7/ %R 10.1007/s10587-011-0029-7 %G en %F 10_1007_s10587_011_0029_7
Das, Pratulananda; Savas, Ekrem; Bhunia, Santanu. Two valued measure and some new double sequence spaces in $2$-normed spaces. Czechoslovak Mathematical Journal, Tome 61 (2011) no. 3, pp. 809-825. doi: 10.1007/s10587-011-0029-7
[1] Bhunia, S., Das, P.: Two valued measure and summability of double sequences in asymmetric context. Acta Math. Hung. 130 (2011), 167-187. | DOI | MR
[2] Colak, R., Et, M., Malkowsky, E.: Strongly almost $(w,\lambda)$-summable sequences defined by Orlicz functions. Hokkaido Math. J. 34 (2005), 265-276. | DOI | MR | Zbl
[3] Connor, J.: Two valued measures and summability. Analysis 10 (1990), 373-385. | DOI | MR | Zbl
[4] Connor, J.: $R$-type summability methods, Cauchy criteria, $P$-sets and statistical convergence. Proc. Am. Math. Soc. 115 (1992), 319-327. | MR | Zbl
[5] Das, P., Malik, P.: On the statistical and $I$ variation of double sequences. Real Anal. Exch. 33 (2008), 351-363. | DOI | MR
[6] Das, P., Kostyrko, P., Wilczyński, W., Malik, P.: $I$ and $I^{*}$-convergence of double sequences. Math. Slovaca 58 (2008), 605-620. | DOI | MR | Zbl
[7] Das, P., Bhunia, S.: Two valued measure and summability of double sequences. Czechoslovak Math. J. 59(134) (2009), 1141-1155. | DOI | MR
[8] Das, P., Malik, P., Savaş, E.: On statistical limit points of double sequences. Appl. Math. Comput. 215 (2009), 1030-1034. | DOI | MR
[9] Fast, H.: Sur la convergence statistique. Colloq. Math. 2 (1951), 241-244. | DOI | MR | Zbl
[10] Fridy, J. A.: On statistical convergence. Analysis 5 (1985), 301-313. | DOI | MR | Zbl
[11] Gähler, S.: 2-metrische Räume und ihre topologische Struktur. Math. Nachr. 26 (1963), 115-148 German. | DOI | MR
[12] Gähler, S.: 2-normed spaces. Math. Nachr. 28 (1964), 1-43.
[13] Gähler, S., Siddiqi, A. H., Gupta, S. C.: Contributions to non-Archimedean functional analysis. Math. Nachr. 69 (1975), 162-171. | MR
[14] Gürdal, M., Pehlivan, S.: Statistical convergence in $2$-normed spaces. Southeast Asian Bull. Math. 33 (2009), 257-264. | MR
[15] Gürdal, M., Sahiner, A., Açik, I.: Approximation theory in 2-Banach spaces. Nolinear Anal., Theory Methods Appl., Ser. A, Theory Methods 71 (2009), 1654-1661. | DOI | MR
[16] Krasnosel'skij, M. A., Rutiskij, Y. B.: Convex Functions and Orlicz Spaces. P. Noordhoff Ltd. Groningen (1961). | MR
[17] Maddox, I. J.: Sequence spaces defined by a modulus. Math. Proc. Camb. Philos. Soc. 100 (1986), 161-166. | DOI | MR | Zbl
[18] Maddox, I. J.: Elements of Functional Analysis. Cambridge University Press Cambridge (1970). | MR | Zbl
[19] Móricz, F.: Statistical convergence of multiple sequences. Arch. Math. 81 (2003), 82-89. | DOI | MR
[20] Mursaleen, Edely, O. H. H.: Statistical convergence of double sequences. J. Math. Anal. Appl. 288 (2003), 223-231. | DOI | MR | Zbl
[21] Nuray, F., Ruckle, W. H.: Generalized statistical convergence and convergence free spaces. J. Math. Anal. Appl. 245 (2000), 513-527. | DOI | MR | Zbl
[22] Parashar, S. D., Choudhary, B.: Sequence spaces defined by Orlicz functions. Indian J. Pure Appl. Math. 25 (1994), 419-428. | MR | Zbl
[23] Pringsheim, A.: Zur Theorie der zweifach unendlichen Zahlenfolgen. Math. Ann. 53 (1900), 289-321 German. | DOI | MR
[24] Ruckle, W. H.: $FK$ spaces in which the sequence of coordinate vectors is bounded. Canad. J. Math. 25 (1973), 973-978. | DOI | MR | Zbl
[25] Sahiner, A., Gürdal, M., Saltan, S., Gunawan, H.: Ideal convergence in 2-normed spaces. Taiwanese J. Math. 11 (2007), 1477-1484. | DOI | MR
[26] Šalát, T.: On statistically convergent sequences of real numbers. Math. Slovaca 30 (1980), 139-150. | MR
[27] Savaş, E., Mursaleen: On statistically convergent double sequences of fuzzy numbers. Inf. Sci. 162 (2004), 183-192. | DOI | MR
[28] Savaş, E., Patterson, R. F.: An Orlicz extension of some new sequences spaces. Rend. Ist. Mat. Univ. Trieste 37 (2005), 145-154. | MR
[29] Savaş, E., Rhoades, B. E.: Double absolute summability factor theorems and applications. Nonlinear Anal., Theory Methods Appl. 69 (2008), 189-200. | MR
[30] Schoenberg, I. J.: The integrability of certain functions and related summability methods. Am. Math. Mon. 66 (1959), 361-375, 562-563. | DOI | MR | Zbl
Cité par Sources :