On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence
Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 194-198

Voir la notice de l'article provenant de la source Cambridge University Press

The definition of strong Cesaro summability with respect to a modulus is extended to a definition of strong A -summability with respect to a modulus when A is a nonnegative regular matrix summability method. It is shown that if a sequence is strongly A-summable with respect to an arbitrary modulus then it is A-statistically convergent and that Astatistical convergence and strong A-summability with respect to a modulus are equivalent on the bounded sequences.
DOI : 10.4153/CMB-1989-029-3
Mots-clés : 40D25, 40A05
Connor, Jeff. On Strong Matrix Summability with Respect to a Modulus and Statistical Convergence. Canadian mathematical bulletin, Tome 32 (1989) no. 2, pp. 194-198. doi: 10.4153/CMB-1989-029-3
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[1] 1. Connor, J., The statistical and strong p-Cesaro convergence of sequences, Analysis, to appear. Google Scholar

[2] 2. Connor, J. and Loomis, I., Linear isometries on subalgebras of l which contain Co, in preparation. Google Scholar

[3] 3. Connor, J., Summabillity methods associated with ideals of bounded sequences, under review. Google Scholar

[4] 4. Fast, H., Sur la convergence statistique, Colloq. Math. 2 (1951). Google Scholar

[5] 5. Flemming, R. and Jamison, J., Hermitian operators and isometries on sums ofBanach spaces, preprint. Google Scholar

[6] 6. Fridy, J., On statistical convergence, Analysis 5, 301–310. Google Scholar

[7] 7. Freedman, A. R. and Sember, J. J., Densities and summability, Pacific J. Math. 95 (1981), 293-305. Google Scholar

[8] 8. Halmos, P., Lectures on Ergodic Theory, Chelsea, 1956. Google Scholar

[9] 9. Hardy, G. H. and Littlewood, J. E., Sur la série d'une function à carré sommable, Comptes Rendus 156 (1913), 1307–9. Google Scholar

[10] 10. Leindler, L. Strong approximation by Fourier series, Akademiai Kiado, Budapest, 1985. Google Scholar

[11] 11. Maddox, I. J., Spaces of strongly summable sequences, Quart. J. Math. Oxford(2) 18 (1967) 345–55. Google Scholar

[12] 12. Maddox, I. J., Sequence spaces defined by a modulus, Math. Proc. Camb. Phil. Soc. 100 (1986), 161–66. Google Scholar

[13] 13. Salat, T. On statistically convergent sequences of real numbers, Math Solvaca 30 (2) (1980), 139–50. Google Scholar

[14] 14. Wilansky, A., Summability through functional analysis, North Holland, 1984. Google Scholar

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