Abstract
In this article we define the notion of statistically convergent difference double sequence spaces. We examine the spaces \( _2 \bar \ell _\infty (\Delta ,q), _2^ - c(\Delta ,q), _2^ - c^B (\Delta ,q), _2^ - c^R (\Delta ,q), _2^ - c^{BR} (\Delta ,q) \) etc. being symmetric, solid, monotone, etc. We prove some inclusion results too.
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References
Bromwich, T. J. IA.: An Introduction to the Theory of Infinite Series, MacMillan & Co. Ltd. New York, 1965
Hardy, G. H.: On the convergence of certain multiple series. Proc. Camb.Phil. Soc., 19, 86–95 (1917)
Moricz, F.: Extension of the spaces c and c 0 from single to double sequences. Acta Math. Hungerica, 57(1–2), 129–136 (1991)
Moricz, F., Rhoades, B. E.: Almost convergence of double sequences and strong regularity of summability matrices. Math. Proc. Camb. Phil. Soc., 104, 283–294 (1988)
Basarir, M., Sonalcan, O.: On some double sequences. J. Indian Acad. Math., 21(2), 193–200 (1999)
Tripathy, B. C.: Statistically convergent double sequences. Tamkang J. Math., 34(3), 321–327 (2003)
Fast, H.: Sur la convergence statistique. Colloq. Math., 2, 241–244 (1951)
Schoenberg, I. J.: The integrability of certain functions and related summability methods. Amer. Math. Monthly, 66, 361–375 (1959)
Zygmund, A.: Trigonometric Series. vol. 2, Cambridge University Press, 1993
Fridy, J. A., Orhan, C.: Statistical limit superior and limit inferior. Proc. Amer. Math. Soc., 125(12), 3625–3631 (1997)
Connor, J. S.: The statistical and strong p-Cesaro convergence of sequences. Analysis, 8, 47–63 (1988)
Rath. D., Tripathy, B. C.: Matrix maps on sequences associated with sets of integers. Indian J. Pure Appl. Math., 27(2), 197–206 (1996)
Salat, T.: On statistically convergent sequences of real numbers. Math. Slovaca, 30(2), 139–150 (1980)
Tripathy, B. C.: Matrix transformation between some classes of sequences. Jour. Math. Anal. Appl., 206(2), 448–450 (1997)
Patterson, R. F.: Analogues of some fundamental theorems of summability theory. Internat. J. Math. Math. Sci., 23(1), 1–9 (2000)
Kizmaz, H.: On certain sequence spaces. Canad. Math. Bull., 24(2), 169–176 (1981)
Tripathy, B. C.: A class of difference sequences related to the p-normed space l p. Demonstratio Math., 36(4), 867–872 (2003)
Tripathy, B. C.: On some classes of difference paranormed sequence spaces associated with multiplier sequences. International Jour. Math., 2(1), 159–166 (2003)
Malkowsky, E., Mursaleen, M., Suantai, S.: The dual spaces of sets of difference sequences of order m and matrix transformations. Acta Mathematica Sinica, English Series, 23(3), 521–532 (2007)
Tripathy, B. C., Sarma, B.: On some classes of difference double sequence spaces. (under communications)
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Tripathy, B.C., Sarma, B. Statistically convergent difference double sequence spaces. Acta. Math. Sin.-English Ser. 24, 737–742 (2008). https://doi.org/10.1007/s10114-007-6648-0
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DOI: https://doi.org/10.1007/s10114-007-6648-0