×

Statistically convergent difference double sequence spaces. (English) Zbl 1160.46003

Summary: We define the notion of statistically convergent difference double sequence spaces. We examine the spaces \(_2 \overline{\ell}_\infty (\Delta ,q), \overline{_2c}(\Delta ,q),\overline{_2c}^B (\Delta ,q), \overline{_2c}^R (\Delta ,q), \overline{_2c}^{BR} (\Delta ,q)\), etc.,being symmetric, solid, monotone, etc. We prove some inclusion results, too.

MSC:

46A45 Sequence spaces (including Köthe sequence spaces)
40A05 Convergence and divergence of series and sequences
40G99 Special methods of summability
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Bromwich, T. J. IA.: An Introduction to the Theory of Infinite Series, MacMillan & Co. Ltd. New York, 1965 · Zbl 0004.00705
[2] Hardy, G. H.: On the convergence of certain multiple series. Proc. Camb.Phil. Soc., 19, 86–95 (1917)
[3] Moricz, F.: Extension of the spaces c and c 0 from single to double sequences. Acta Math. Hungerica, 57(1–2), 129–136 (1991) · Zbl 0781.46025
[4] 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) · Zbl 0675.40004
[5] Basarir, M., Sonalcan, O.: On some double sequences. J. Indian Acad. Math., 21(2), 193–200 (1999) · Zbl 0978.40002
[6] Tripathy, B. C.: Statistically convergent double sequences. Tamkang J. Math., 34(3), 321–327 (2003) · Zbl 1040.40001
[7] Fast, H.: Sur la convergence statistique. Colloq. Math., 2, 241–244 (1951) · Zbl 0044.33605
[8] Schoenberg, I. J.: The integrability of certain functions and related summability methods. Amer. Math. Monthly, 66, 361–375 (1959) · Zbl 0089.04002
[9] Zygmund, A.: Trigonometric Series. vol. 2, Cambridge University Press, 1993 · JFM 58.0296.09
[10] Fridy, J. A., Orhan, C.: Statistical limit superior and limit inferior. Proc. Amer. Math. Soc., 125(12), 3625–3631 (1997) · Zbl 0883.40003
[11] Connor, J. S.: The statistical and strong p-Cesaro convergence of sequences. Analysis, 8, 47–63 (1988) · Zbl 0653.40001
[12] Rath. D., Tripathy, B. C.: Matrix maps on sequences associated with sets of integers. Indian J. Pure Appl. Math., 27(2), 197–206 (1996) · Zbl 0843.47017
[13] Salat, T.: On statistically convergent sequences of real numbers. Math. Slovaca, 30(2), 139–150 (1980) · Zbl 0437.40003
[14] Tripathy, B. C.: Matrix transformation between some classes of sequences. Jour. Math. Anal. Appl., 206(2), 448–450 (1997) · Zbl 0907.47021
[15] Patterson, R. F.: Analogues of some fundamental theorems of summability theory. Internat. J. Math. Math. Sci., 23(1), 1–9 (2000) · Zbl 0954.40005
[16] Kizmaz, H.: On certain sequence spaces. Canad. Math. Bull., 24(2), 169–176 (1981) · Zbl 0454.46010
[17] Tripathy, B. C.: A class of difference sequences related to the p-normed space l p. Demonstratio Math., 36(4), 867–872 (2003) · Zbl 1042.40001
[18] Tripathy, B. C.: On some classes of difference paranormed sequence spaces associated with multiplier sequences. International Jour. Math., 2(1), 159–166 (2003) · Zbl 1064.40002
[19] 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) · Zbl 1123.46007
[20] Tripathy, B. C., Sarma, B.: On some classes of difference double sequence spaces. (under communications) · Zbl 1177.46008
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.